各位の数字にゼロが現れない数を英語圏では “zeroless number“（ゼロレスナンバー）と呼びます。zeroless数であるような累乗数を「zeroless累乗数」と言います。
zeroless累乗数の指数の最大値
zeroless累乗数のうち、指数の最大値を2～99までの底ごとにまとめると以下の表のようになります。なお、$10$の倍数を底とする累乗数にzeroless数は存在しないので省いています（ゼロ乗は除いています）。
表．zeroless累乗数の指数の最大値
| 底 | 指数 | 底 | 指数 | 底 | 指数 |
| 2 | 86 | 36 | 22 | 71 | 8 |
| 3 | 68 | 37 | 16 | 72 | 22 |
| 4 | 43 | 38 | 10 | 73 | 6 |
| 5 | 58 | 39 | 19 | 74 | 4 |
| 6 | 44 | 41 | 9 | 75 | 19 |
| 7 | 35 | 42 | 13 | 76 | 11 |
| 8 | 27 | 43 | 10 | 77 | 12 |
| 9 | 34 | 44 | 6 | 78 | 10 |
| 11 | 41 | 45 | 39 | 79 | 9 |
| 12 | 26 | 46 | 7 | 80 | 0 |
| 13 | 14 | 47 | 8 | 81 | 17 |
| 14 | 34 | 48 | 19 | 82 | 13 |
| 15 | 27 | 49 | 5 | 83 | 4 |
| 16 | 19 | 51 | 19 | 84 | 18 |
| 17 | 27 | 52 | 18 | 85 | 11 |
| 18 | 17 | 53 | 7 | 86 | 12 |
| 19 | 44 | 54 | 13 | 87 | 10 |
| 21 | 13 | 55 | 11 | 88 | 5 |
| 22 | 22 | 56 | 23 | 89 | 23 |
| 23 | 10 | 57 | 7 | 90 | 0 |
| 24 | 13 | 58 | 23 | 91 | 19 |
| 25 | 29 | 59 | 14 | 92 | 10 |
| 26 | 15 | 61 | 16 | 93 | 5 |
| 27 | 9 | 62 | 5 | 94 | 15 |
| 28 | 16 | 63 | 14 | 95 | 3 |
| 29 | 14 | 64 | 12 | 96 | 8 |
| 31 | 16 | 65 | 3 | 97 | 8 |
| 32 | 7 | 66 | 14 | 98 | 19 |
| 33 | 23 | 67 | 14 | 99 | 19 |
| 34 | 5 | 68 | 14 | ||
| 35 | 17 | 69 | 12 |
zeroless累乗数のリスト
以下、zeroless数であるような累乗数「zeroless累乗数」を一覧にしています。
$2^{1} = 2$
$2^{2} = 4$
$2^{3} = 8$
$2^{4} = 16$
$2^{5} = 32$
$2^{6} = 64$
$2^{7} = 128$
$2^{8} = 256$
$2^{9} = 512$
$2^{13} = 8192$
$2^{14} = 16384$
$2^{15} = 32768$
$2^{16} = 65536$
$2^{18} = 262144$
$2^{19} = 524288$
$2^{24} = 16777216$
$2^{25} = 33554432$
$2^{27} = 134217728$
$2^{28} = 268435456$
$2^{31} = 2147483648$
$2^{32} = 4294967296$
$2^{33} = 8589934592$
$2^{34} = 17179869184$
$2^{35} = 34359738368$
$2^{36} = 68719476736$
$2^{37} = 137438953472$
$2^{39} = 549755813888$
$2^{49} = 562949953421312$
$2^{51} = 2251799813685248$
$2^{67} = 147573952589676412928$
$2^{72} = 4722366482869645213696$
$2^{76} = 75557863725914323419136$
$2^{77} = 151115727451828646838272$
$2^{81} = 2417851639229258349412352$
$2^{86} = 77371252455336267181195264$
以上35個
$3^{1} = 3$
$3^{2} = 9$
$3^{3} = 27$
$3^{4} = 81$
$3^{5} = 243$
$3^{6} = 729$
$3^{7} = 2187$
$3^{8} = 6561$
$3^{9} = 19683$
$3^{11} = 177147$
$3^{12} = 531441$
$3^{13} = 1594323$
$3^{14} = 4782969$
$3^{19} = 1162261467$
$3^{23} = 94143178827$
$3^{24} = 282429536481$
$3^{26} = 2541865828329$
$3^{27} = 7625597484987$
$3^{28} = 22876792454961$
$3^{31} = 617673396283947$
$3^{34} = 16677181699666569$
$3^{68} = 278128389443693511257285776231761$
以上22個
$4^{1} = 4$
$4^{2} = 16$
$4^{3} = 64$
$4^{4} = 256$
$4^{7} = 16384$
$4^{8} = 65536$
$4^{9} = 262144$
$4^{12} = 16777216$
$4^{14} = 268435456$
$4^{16} = 4294967296$
$4^{17} = 17179869184$
$4^{18} = 68719476736$
$4^{36} = 4722366482869645213696$
$4^{38} = 75557863725914323419136$
$4^{43} = 77371252455336267181195264$
以上15個
$5^{1} = 5$
$5^{2} = 25$
$5^{3} = 125$
$5^{4} = 625$
$5^{5} = 3125$
$5^{6} = 15625$
$5^{7} = 78125$
$5^{9} = 1953125$
$5^{10} = 9765625$
$5^{11} = 48828125$
$5^{17} = 762939453125$
$5^{18} = 3814697265625$
$5^{30} = 931322574615478515625$
$5^{33} = 116415321826934814453125$
$5^{58} = 34694469519536141888238489627838134765625$
以上15個
$6^{1} = 6$
$6^{2} = 36$
$6^{3} = 216$
$6^{4} = 1296$
$6^{5} = 7776$
$6^{6} = 46656$
$6^{7} = 279936$
$6^{8} = 1679616$
$6^{12} = 2176782336$
$6^{17} = 16926659444736$
$6^{24} = 4738381338321616896$
$6^{29} = 36845653286788892983296$
$6^{44} = 17324272922341479351919144385642496$
以上13個
$7^{1} = 7$
$7^{2} = 49$
$7^{3} = 343$
$7^{6} = 117649$
$7^{7} = 823543$
$7^{10} = 282475249$
$7^{11} = 1977326743$
$7^{19} = 11398895185373143$
$7^{35} = 378818692265664781682717625943$
以上9個
$8^{1} = 8$
$8^{2} = 64$
$8^{3} = 512$
$8^{5} = 32768$
$8^{6} = 262144$
$8^{8} = 16777216$
$8^{9} = 134217728$
$8^{11} = 8589934592$
$8^{12} = 68719476736$
$8^{13} = 549755813888$
$8^{17} = 2251799813685248$
$8^{24} = 4722366482869645213696$
$8^{27} = 2417851639229258349412352$
以上13個
$9^{1} = 9$
$9^{2} = 81$
$9^{3} = 729$
$9^{4} = 6561$
$9^{6} = 531441$
$9^{7} = 4782969$
$9^{12} = 282429536481$
$9^{13} = 2541865828329$
$9^{14} = 22876792454961$
$9^{17} = 16677181699666569$
$9^{34} = 278128389443693511257285776231761$
以上11個
$11^{1} = 11$
$11^{2} = 121$
$11^{3} = 1331$
$11^{4} = 14641$
$11^{6} = 1771561$
$11^{7} = 19487171$
$11^{8} = 214358881$
$11^{9} = 2357947691$
$11^{12} = 3138428376721$
$11^{13} = 34522712143931$
$11^{14} = 379749833583241$
$11^{15} = 4177248169415651$
$11^{16} = 45949729863572161$
$11^{18} = 5559917313492231481$
$11^{41} = 4978518112499354698647829163838661251242411$
以上15個
$12^{1} = 12$
$12^{2} = 144$
$12^{3} = 1728$
$12^{5} = 248832$
$12^{6} = 2985984$
$12^{8} = 429981696$
$12^{10} = 61917364224$
$12^{14} = 1283918464548864$
$12^{20} = 3833759992447475122176$
$12^{26} = 11447545997288281555215581184$
以上10個
$13^{1} = 13$
$13^{2} = 169$
$13^{3} = 2197$
$13^{4} = 28561$
$13^{5} = 371293$
$13^{7} = 62748517$
$13^{10} = 137858491849$
$13^{14} = 3937376385699289$
以上8個
$14^{1} = 14$
$14^{2} = 196$
$14^{3} = 2744$
$14^{4} = 38416$
$14^{5} = 537824$
$14^{6} = 7529536$
$14^{10} = 289254654976$
$14^{12} = 56693912375296$
$14^{13} = 793714773254144$
$14^{28} = 123476695691247935826229781856256$
$14^{34} = 929722225368296217729286886758826377216$
以上11個
$15^{1} = 15$
$15^{2} = 225$
$15^{3} = 3375$
$15^{5} = 759375$
$15^{9} = 38443359375$
$15^{11} = 8649755859375$
$15^{17} = 98526125335693359375$
$15^{27} = 56815128661595284938812255859375$
以上8個
$16^{1} = 16$
$16^{2} = 256$
$16^{4} = 65536$
$16^{6} = 16777216$
$16^{7} = 268435456$
$16^{8} = 4294967296$
$16^{9} = 68719476736$
$16^{18} = 4722366482869645213696$
$16^{19} = 75557863725914323419136$
以上9個
$17^{1} = 17$
$17^{2} = 289$
$17^{3} = 4913$
$17^{4} = 83521$
$17^{5} = 1419857$
$17^{6} = 24137569$
$17^{8} = 6975757441$
$17^{9} = 118587876497$
$17^{12} = 582622237229761$
$17^{16} = 48661191875666868481$
$17^{27} = 1667711322168688287513535727415473$
以上11個
$18^{1} = 18$
$18^{2} = 324$
$18^{3} = 5832$
$18^{5} = 1889568$
$18^{12} = 1156831381426176$
$18^{17} = 2185911559738696531968$
以上6個
$19^{1} = 19$
$19^{2} = 361$
$19^{3} = 6859$
$19^{7} = 893871739$
$19^{9} = 322687697779$
$19^{16} = 288441413567621167681$
$19^{44} = 184144368549628275143663229532787625188711914273876985521$
以上7個
$21^{1} = 21$
$21^{2} = 441$
$21^{3} = 9261$
$21^{4} = 194481$
$21^{6} = 85766121$
$21^{8} = 37822859361$
$21^{12} = 7355827511386641$
$21^{13} = 154472377739119461$
以上8個
$22^{1} = 22$
$22^{2} = 484$
$22^{4} = 234256$
$22^{5} = 5153632$
$22^{7} = 2494357888$
$22^{8} = 54875873536$
$22^{10} = 26559922791424$
$22^{17} = 66249952919459433152512$
$22^{22} = 341427877364219557396646723584$
以上9個
$23^{1} = 23$
$23^{2} = 529$
$23^{3} = 12167$
$23^{4} = 279841$
$23^{5} = 6436343$
$23^{10} = 41426511213649$
以上6個
$24^{1} = 24$
$24^{2} = 576$
$24^{3} = 13824$
$24^{4} = 331776$
$24^{5} = 7962624$
$24^{7} = 4586471424$
$24^{13} = 876488338465357824$
以上7個
$25^{1} = 25$
$25^{2} = 625$
$25^{3} = 15625$
$25^{5} = 9765625$
$25^{9} = 3814697265625$
$25^{15} = 931322574615478515625$
$25^{29} = 34694469519536141888238489627838134765625$
以上7個
$26^{1} = 26$
$26^{2} = 676$
$26^{3} = 17576$
$26^{4} = 456976$
$26^{5} = 11881376$
$26^{12} = 95428956661682176$
$26^{15} = 1677259342285725925376$
以上7個
$27^{1} = 27$
$27^{2} = 729$
$27^{3} = 19683$
$27^{4} = 531441$
$27^{8} = 282429536481$
$27^{9} = 7625597484987$
以上6個
$28^{1} = 28$
$28^{2} = 784$
$28^{3} = 21952$
$28^{4} = 614656$
$28^{7} = 13492928512$
$28^{10} = 296196766695424$
$28^{16} = 142734349946674946768896$
以上7個
$29^{1} = 29$
$29^{2} = 841$
$29^{3} = 24389$
$29^{6} = 594823321$
$29^{14} = 297558232675799463481$
以上5個
$31^{1} = 31$
$31^{2} = 961$
$31^{3} = 29791$
$31^{4} = 923521$
$31^{5} = 28629151$
$31^{7} = 27512614111$
$31^{12} = 787662783788549761$
$31^{15} = 23465261991844685929951$
$31^{16} = 727423121747185263828481$
以上9個
$32^{1} = 32$
$32^{3} = 32768$
$32^{5} = 33554432$
$32^{7} = 34359738368$
以上4個
$33^{1} = 33$
$33^{3} = 35937$
$33^{4} = 1185921$
$33^{5} = 39135393$
$33^{6} = 1291467969$
$33^{7} = 42618442977$
$33^{10} = 1531578985264449$
$33^{12} = 1667889514952984961$
$33^{17} = 65273511648264442971824673$
$33^{23} = 84298649517881922539738734663399137$
以上10個
$34^{1} = 34$
$34^{2} = 1156$
$34^{4} = 1336336$
$34^{5} = 45435424$
以上4個
$35^{1} = 35$
$35^{2} = 1225$
$35^{3} = 42875$
$35^{5} = 52521875$
$35^{6} = 1838265625$
$35^{7} = 64339296875$
$35^{9} = 78815638671875$
$35^{10} = 2758547353515625$
$35^{13} = 118272717781982421875$
$35^{14} = 4139545122369384765625$
$35^{17} = 177482997121587371826171875$
以上11個
$36^{1} = 36$
$36^{2} = 1296$
$36^{3} = 46656$
$36^{4} = 1679616$
$36^{6} = 2176782336$
$36^{12} = 4738381338321616896$
$36^{22} = 17324272922341479351919144385642496$
以上7個
$37^{1} = 37$
$37^{2} = 1369$
$37^{4} = 1874161$
$37^{5} = 69343957$
$37^{7} = 94931877133$
$37^{8} = 3512479453921$
$37^{16} = 12337511914217166362274241$
以上7個
$38^{1} = 38$
$38^{2} = 1444$
$38^{3} = 54872$
$38^{5} = 79235168$
$38^{7} = 114415582592$
$38^{8} = 4347792138496$
$38^{10} = 6278211847988224$
以上7個
$39^{1} = 39$
$39^{2} = 1521$
$39^{3} = 59319$
$39^{4} = 2313441$
$39^{6} = 3518743761$
$39^{11} = 317475837322472439$
$39^{12} = 12381557655576425121$
$39^{15} = 734461618571137961752599$
$39^{19} = 1699133621328831977374894383159$
以上9個
$41^{1} = 41$
$41^{2} = 1681$
$41^{3} = 68921$
$41^{4} = 2825761$
$41^{7} = 194754273881$
$41^{8} = 7984925229121$
$41^{9} = 327381934393961$
以上7個
$42^{1} = 42$
$42^{2} = 1764$
$42^{4} = 3111696$
$42^{8} = 9682651996416$
$42^{13} = 1265437718438866624512$
以上5個
$43^{1} = 43$
$43^{2} = 1849$
$43^{10} = 21611482313284249$
以上3個
$44^{1} = 44$
$44^{2} = 1936$
$44^{3} = 85184$
$44^{5} = 164916224$
$44^{6} = 7256313856$
以上5個
$45^{1} = 45$
$45^{3} = 91125$
$45^{5} = 184528125$
$45^{7} = 373669453125$
$45^{18} = 572565594852444156646728515625$
$45^{39} = 29873632717245815267654448326919473927773651666939258575439453125$
以上6個
$46^{1} = 46$
$46^{2} = 2116$
$46^{3} = 97336$
$46^{4} = 4477456$
$46^{6} = 9474296896$
$46^{7} = 435817657216$
以上6個
$47^{1} = 47$
$47^{4} = 4879681$
$47^{8} = 23811286661761$
以上3個
$48^{1} = 48$
$48^{14} = 344649238497994142121984$
$48^{19} = 87817993537467267453437463232512$
以上3個
$49^{1} = 49$
$49^{3} = 117649$
$49^{5} = 282475249$
以上3個
$51^{1} = 51$
$51^{3} = 132651$
$51^{19} = 277864679818687128933845596553451$
以上3個
$52^{1} = 52$
$52^{4} = 7311616$
$52^{8} = 53459728531456$
$52^{18} = 7727876721872448746791521746944$
以上4個
$53^{1} = 53$
$53^{3} = 148877$
$53^{5} = 418195493$
$53^{6} = 22164361129$
$53^{7} = 1174711139837$
以上5個
$54^{1} = 54$
$54^{2} = 2916$
$54^{3} = 157464$
$54^{6} = 24794911296$
$54^{13} = 33198531813531453579264$
以上5個
$55^{1} = 55$
$55^{3} = 166375$
$55^{7} = 1522435234375$
$55^{11} = 13931233916552734375$
以上4個
$56^{1} = 56$
$56^{2} = 3136$
$56^{3} = 175616$
$56^{4} = 9834496$
$56^{9} = 5416169448144896$
$56^{14} = 2982856619293778479415296$
$56^{23} = 16155656889615734329398214425629966729216$
以上7個
$57^{1} = 57$
$57^{2} = 3249$
$57^{3} = 185193$
$57^{6} = 34296447249$
$57^{7} = 1954897493193$
以上5個
$58^{1} = 58$
$58^{2} = 3364$
$58^{3} = 195112$
$58^{4} = 11316496$
$58^{5} = 656356768$
$58^{9} = 7427658739644928$
$58^{23} = 36211277946678491129762594928113653645312$
以上7個
$59^{1} = 59$
$59^{2} = 3481$
$59^{4} = 12117361$
$59^{5} = 714924299$
$59^{7} = 2488651484819$
$59^{9} = 8662995818654939$
$59^{12} = 1779197418239532716881$
$59^{14} = 6193386212891813387462761$
以上8個
$61^{1} = 61$
$61^{2} = 3721$
$61^{3} = 226981$
$61^{4} = 13845841$
$61^{11} = 43513917611435838661$
$61^{12} = 2654348974297586158321$
$61^{13} = 161915287432152755657581$
$61^{16} = 36751693856637464631913392961$
以上8個
$62^{1} = 62$
$62^{2} = 3844$
$62^{3} = 238328$
$62^{4} = 14776336$
$62^{5} = 916132832$
以上5個
$63^{1} = 63$
$63^{2} = 3969$
$63^{4} = 15752961$
$63^{5} = 992436543$
$63^{9} = 15633814156853823$
$63^{14} = 15515568475732467854453889$
以上6個
$64^{1} = 64$
$64^{3} = 262144$
$64^{4} = 16777216$
$64^{6} = 68719476736$
$64^{12} = 4722366482869645213696$
以上5個
$65^{1} = 65$
$65^{2} = 4225$
$65^{3} = 274625$
以上3個
$66^{1} = 66$
$66^{2} = 4356$
$66^{3} = 287496$
$66^{4} = 18974736$
$66^{5} = 1252332576$
$66^{14} = 29758778274345789399515136$
以上6個
$67^{1} = 67$
$67^{2} = 4489$
$67^{14} = 36732225162896895721934329$
以上3個
$68^{1} = 68$
$68^{2} = 4624$
$68^{3} = 314432$
$68^{4} = 21381376$
$68^{5} = 1453933568$
$68^{6} = 98867482624$
$68^{7} = 6722988818432$
$68^{8} = 457163239653376$
$68^{14} = 45198578652761699462938624$
以上9個
$69^{1} = 69$
$69^{2} = 4761$
$69^{4} = 22667121$
$69^{7} = 7446353252589$
$69^{8} = 513798374428641$
$69^{12} = 11646329922777311412561$
以上6個
$71^{1} = 71$
$71^{3} = 357911$
$71^{4} = 25411681$
$71^{8} = 645753531245761$
以上4個
$72^{1} = 72$
$72^{2} = 5184$
$72^{3} = 373248$
$72^{4} = 26873856$
$72^{5} = 1934917632$
$72^{9} = 51998697814228992$
$72^{22} = 72663267215268556211671874973277863542784$
以上7個
$73^{1} = 73$
$73^{2} = 5329$
$73^{4} = 28398241$
$73^{6} = 151334226289$
以上4個
$74^{1} = 74$
$74^{2} = 5476$
$74^{4} = 29986576$
以上3個
$75^{1} = 75$
$75^{2} = 5625$
$75^{3} = 421875$
$75^{6} = 177978515625$
$75^{7} = 13348388671875$
$75^{19} = 422828258524532429873943328857421875$
以上6個
$76^{1} = 76$
$76^{2} = 5776$
$76^{3} = 438976$
$76^{4} = 33362176$
$76^{5} = 2535525376$
$76^{6} = 192699928576$
$76^{7} = 14645194571776$
$76^{10} = 6428888932339941376$
$76^{11} = 488595558857835544576$
以上9個
$77^{1} = 77$
$77^{2} = 5929$
$77^{3} = 456533$
$77^{8} = 1235736291547681$
$77^{9} = 95151694449171437$
$77^{11} = 564154396389137449973$
$77^{12} = 43439888521963583647921$
以上7個
$78^{1} = 78$
$78^{3} = 474552$
$78^{5} = 2887174368$
$78^{7} = 17565568854912$
$78^{10} = 8335775831236199424$
以上5個
$79^{1} = 79$
$79^{2} = 6241$
$79^{9} = 119851595982618319$
以上3個
$81^{1} = 81$
$81^{2} = 6561$
$81^{3} = 531441$
$81^{6} = 282429536481$
$81^{7} = 22876792454961$
$81^{17} = 278128389443693511257285776231761$
以上6個
$82^{1} = 82$
$82^{2} = 6724$
$82^{3} = 551368$
$82^{4} = 45212176$
$82^{13} = 7578444614164591651397632$
以上5個
$83^{1} = 83$
$83^{2} = 6889$
$83^{3} = 571787$
$83^{4} = 47458321$
以上4個
$84^{1} = 84$
$84^{4} = 49787136$
$84^{5} = 4182119424$
$84^{18} = 43353797936295338532183652115152896$
以上4個
$85^{1} = 85$
$85^{2} = 7225$
$85^{3} = 614125$
$85^{6} = 377149515625$
$85^{11} = 1673432436896142578125$
以上5個
$86^{1} = 86$
$86^{2} = 7396$
$86^{7} = 34792782221696$
$86^{9} = 257327417311663616$
$86^{12} = 163674647745587512938496$
以上5個
$87^{1} = 87$
$87^{2} = 7569$
$87^{4} = 57289761$
$87^{7} = 37725479487783$
$87^{8} = 3282116715437121$
$87^{10} = 24842341419143568849$
以上6個
$88^{1} = 88$
$88^{2} = 7744$
$88^{3} = 681472$
$88^{4} = 59969536$
$88^{5} = 5277319168$
以上5個
$89^{1} = 89$
$89^{2} = 7921$
$89^{4} = 62742241$
$89^{7} = 44231334895529$
$89^{23} = 685441117453157943684715454813971461595561769$
以上5個
$91^{1} = 91$
$91^{2} = 8281$
$91^{3} = 753571$
$91^{4} = 68574961$
$91^{11} = 3543686674874777831491$
$91^{19} = 16664276159359979836134597478321347811$
以上6個
$92^{1} = 92$
$92^{2} = 8464$
$92^{3} = 778688$
$92^{4} = 71639296$
$92^{8} = 5132188731375616$
$92^{9} = 472161363286556672$
$92^{10} = 43438845422363213824$
以上7個
$93^{1} = 93$
$93^{2} = 8649$
$93^{5} = 6956883693$
以上3個
$94^{1} = 94$
$94^{2} = 8836$
$94^{7} = 64847759419264$
$94^{15} = 395291798759681826446224359424$
以上4個
$95^{1} = 95$
$95^{3} = 857375$
以上2個
$96^{1} = 96$
$96^{2} = 9216$
$96^{3} = 884736$
$96^{4} = 84934656$
$96^{5} = 8153726976$
$96^{6} = 782757789696$
$96^{8} = 7213895789838336$
以上7個
$97^{1} = 97$
$97^{3} = 912673$
$97^{4} = 88529281$
$97^{8} = 7837433594376961$
以上4個
$98^{1} = 98$
$98^{3} = 941192$
$98^{4} = 92236816$
$98^{7} = 86812553324672$
$98^{19} = 68123262423989233971191949923948429312$
以上5個
$99^{1} = 99$
$99^{17} = 8429431933839268832485642678641699$
$99^{19} = 82616862383558673827191783893367291899$
以上3個