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gapful numbers
L.Colucci calls a number  $n$  of at least 3 digits a gapful number if  $n$  is divisible by the number formed by the first and last digit of  $n$.

For example, 583 is gapful because it is divisible by 53.

About the 7.46% of the numbers are gapful.

The smallest Pythagorean triple made of gapful numbers is (100, 120, 200) and the first such primitive triple is (3159, 29440, 29609).

The concept can be extended to other bases. For example, the number 240 is gapful in all the bases from 2 to 10 and the number 54288 is gapful in all the bases from 2 to 16.

The first gapful numbers are 100, 105, 108, 110, 120, 121, 130, 132, 135, 140, 143, 150, 154, 160, 165, 170, 176, 180, 187, 190, 192, 195, 198, 200, 220, 225, 231, 240, 242, 253 more terms

Gapful numbers can also be... (you may click on names or numbers and on + to get more values)

ABA 160 192 200 + 100000000000 aban 100 105 108 + 100000000000 abundant 100 108 120 + 50000000 Achilles 108 200 500 + 99999796428 admirable 120 140 1204 + 69989072 alternating 105 121 143 + 989898765 amenable 100 105 108 + 1000000000 amicable 220 1210 2620 + 98735418525 apocalyptic 192 220 286 + 30000 arithmetic 105 110 132 + 9999990 astonishing 3078 20328 21252 + 38788281213 automorphic 109376 2890625 12890625 + 1787109376 Bell 4213597 betrothed 140 195 1050 + 20322463175 binomial 105 120 165 + 99994143600 brilliant 121 143 187 + 2059 c.decagonal 451 781 4961 + 79965084161 c.heptagonal 253 1331 24403 + 99842279272 c.nonagonal 190 253 1540 + 99969549085 c.octagonal 121 225 2025 + 99965365929 c.pentagonal 11056 36301 55131 + 99906521856 c.square 4141 6161 21425 + 89971547405 c.triangular 4960 9964 10210 + 99991177735 cake 130 176 1160 + 99739632104 Carmichael 561 1729 41041 + 99678195865 Catalan 132 1430 2674440 + 24466267020 compositorial 192 1728 17280 + 12541132800 congruent 110 120 135 + 9999990 constructible 120 160 170 + 86236206080 cube 1000 1331 1728 + 99961946721 Cullen 385 10241 1048577 + 32212254721 Cunningham 120 143 170 + 99992558655 Curzon 105 165 198 + 199999965 cyclic 143 187 341 + 9999985 D-number 195 315 693 + 6999363 d-powerful 132 135 264 + 9999827 de Polignac 1207 6161 10021 + 99999755 decagonal 297 451 1540 + 99997143840 deceptive 451 1729 3367 + 98902683061 deficient 105 110 121 + 9999985 dig.balanced 108 120 135 + 199999936 double fact. 105 3840 10395 + 81749606400 droll 240 800 2240 + 98524200960 Duffinian 100 121 143 + 9999827 eban 2000 2002 2040 + 66066066066 economical 105 121 135 + 20000000 emirpimes 143 187 341 + 99990607 enlightened 2304 2500 2560 + 25711938560 equidigital 105 121 135 + 19999750 eRAP 170 1274 10620 + 99996379650 esthetic 121 1010 1210 + 98987676567 Eulerian 120 47840 131054 + 14875399450 evil 105 108 120 + 1000000001 factorial 120 40320 362880 + 87178291200 fibodiv 13010 14311 15612 + 11240023125 Fibonacci 46368 14930352 102334155 + 4807526976 Friedman 121 1260 1296 + 992256 frugal 1215 1250 1280 + 999937953 Gilda 110 220 330 + 1377313380 happy 100 130 176 + 10000000 harmonic 140 1638 18600 + 95300150400 Harshad 100 108 110 + 10000000000 heptagonal 286 2059 3367 + 99994700070 hex 3367 64387 90307 + 99963102421 hexagonal 120 190 231 + 99982069551 highly composite 120 180 240 + 97772875200 hoax 160 660 1111 + 99992520 Hogben 12883 16003 17823 + 99992242441 house 10470 20525 120495 + 97790688541 hungry 712201 2401519 hyperperfect 159841 1570153 iban 100 110 120 + 777777 iccanobiF 1053 17354310 21807674140 idoneal 105 120 130 + 1365 impolite 1048576 16777216 33554432 67108864 inconsummate 195 1037 1053 + 999936 insolite 11112 122121216 1111112112 + 32111111232 interprime 105 108 120 + 99999936 Jacobsthal 341 1365 11184811 357913941 Jordan-Polya 120 192 240 + 99632332800 junction 105 315 1001 + 99999360 Kaprekar 297 5050 7272 + 74074074075 katadrome 3210 4320 6420 + 9876543210 Lehmer 451 561 1111 + 99994249447 Leyland 100 4240 16580 + 20000000000 lonely 120 1340 1344 + 25056082300 Lucas 167761 1860498 20633239 lucky 105 135 195 + 9997135 Lynch-Bell 132 135 264 + 9723168 magic 260 671 1695 + 99230675185 magnanimous 110 130 170 + 22226226625 metadrome 135 1245 1278 + 12346789 modest 1030 1037 1090 + 1999889991 Moran 190 195 198 + 59998914 Motzkin 1129760415 narcissistic 1741725 472335975 nialpdrome 100 110 200 + 100000000000 nonagonal 154 396 1216 + 99989105139 nude 132 135 264 + 499999968 O'Halloran 140 260 660 oban 300 315 330 + 990 octagonal 176 225 280 + 99999431280 odious 100 110 121 + 1000000000 palindromic 121 242 363 + 99990009999 pancake 121 154 352 + 99964183412 panconsummate 121 231 pandigital 108 120 135 + 9876543210 partition 135 176 231 + 18440293320 pentagonal 176 330 1001 + 99994534200 pernicious 100 110 121 + 9999985 Perrin 1130 3480 76725 + 5886726725 persistent 1023458769 1023475869 1023567948 + 99876543210 plaindrome 135 225 1111 + 77788888999 Poulet 341 561 1729 + 99909442585 power 100 121 225 + 100000000000 powerful 100 108 121 + 100000000000 practical 100 108 120 + 10000000 prim.abundant 550 572 1204 + 99972015 primeval 1037 10279 100234567 1001234567 primorial 30030 pronic 110 132 240 + 99997934400 Proth 225 385 1665 + 99978051585 pseudoperfect 100 108 120 + 4294901760 repdigit 1111 2222 3333 + 9999999999 repfigit 2580 147640 174680 + 33445755 repunit 121 341 400 + 99992242441 Rhonda 242352 681265 733125 + 99218417257 Ruth-Aaron 105 154 1330 + 99998417493 Saint-Exupery 480 1620 2040 + 99997662240 Sastry 106755 110667555 147928995 + 85677207840 self 108 110 121 + 1000000005 self-describing 4444 442244 666666 + 8888882288 semiprime 121 143 187 + 99990607 sliding 110 200 700 + 81250000000 Smith 121 1111 1376 + 99995670 sphenic 105 110 130 + 99999755 square 100 121 225 + 99997618176 star 121 253 1441 + 99989241337 straight-line 135 1111 2222 + 9999999999 strobogrammatic 1001 1111 1881 + 96969069696 subfactorial 14833 14684570 176214841 super Niven 100 110 120 + 48888000000 super-d 105 190 231 + 9999810 superabundant 120 180 240 + 80313433200 tau 108 132 180 + 1000000000 taxicab 1729 32832 40033 + 99901836125 tetrahedral 120 165 220 + 99668626200 tetranacci 108 1490 147312 + 10312882481 triangular 105 120 190 + 99994143600 tribonacci 19513 223317 29249425 trimorphic 3751 9999 109376 + 36425781249 uban 1000000 1000005 1000008 + 99099000099 Ulam 180 253 260 + 10000214 undulating 121 242 363 + 56565656565 unprimeable 200 1070 1130 + 10000000 untouchable 120 792 1060 + 999990 upside-down 1919 2828 3737 + 89976543112 vampire 1260 1395 1530 + 9953948970 wasteful 100 108 110 + 9999990 weird 10430 10570 10990 + 799610 Wieferich 157995 473985 684645 + 68096845635 Woodall 15624 24575 229375 + 68719476735 Zeisel 105 1729 1012121 + 65092917061 Zuckerman 132 135 315 + 9921911616 Zumkeller 108 120 132 + 100000 zygodrome 1100 1111 1155 + 99999999900