[go: up one dir, main page]
Search a number
nude numbers
Y.Katagiri calls a number nude if it is divisible by all of its digits (which should be nonzero) like  $672=6\cdot112=7\cdot96=2\cdot 336$. (The number is called "nude" because it exposes some of its factors).

There are only 9039 such numbers below one million, however there are infinite nude numbers since all repdigits are nude.

The smallest nude number which contains all the odd digits is 1117935. Note that if a nude number contains a `5', then all the other digits must be odd.

The smallest nude  $n$  which contains the maximal (8) number of distinct digits is 1123449768. The smallest triple of consecutive nontrivial nude numbers is (1111, 1112, 1113). It is easy to see that there cannot be 4 consecutive nude numbers greater than 10.

The smallest 3 × 3 magic square whose entries are nontrivial consecutive nude numbers is

883416883128883344
883224883296883368
883248883464883176

The first nude numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 22, 24, 33, 36, 44, 48, 55, 66, 77, 88, 99, 111, 112, 115, 122, 124, 126, 128 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
remainders of nude numbers

A graph displaying how many nude numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.
divisibility of nude numbers
Useful links R.A.Ribas, The nude numbers
OEIS, Sequence A034838
Nude numbers can also be... (you may click on names or numbers and on + to get more values)

a-pointer 11 ABA 24 128 162 + 496881288 aban 11 12 15 + 999 abundant 12 24 36 + 49999968 Achilles 288 432 648 + 498389976 admirable 12 24 66 + 88828144 alternating 12 36 212 + 498989232 amenable 12 24 33 + 499999968 amicable 1184 anti-perfect 244 apocalyptic 222 224 312 + 29916 arithmetic 11 15 22 + 9999999 astonishing 15 216 7119 Bell 15 betrothed 48 1575 5775 binomial 15 36 55 + 488234376 brilliant 15 c.decagonal 11 c.heptagonal 22 811448 12882248 22111888 c.nonagonal 55 8128 881128 + 127241128 c.pentagonal 1266 1626 6126 + 211163226 c.triangular 2224 11224 22144 + 421421824 cake 15 12384 1848448 + 264888384 Catalan 132 Chen 11 compositorial 24 congruent 15 22 24 + 9999999 constructible 12 15 24 + 26843136 cube 216 2744 13824 + 463684824 Cunningham 15 24 33 + 496621224 Curzon 33 366 1626 + 199996326 cyclic 11 15 33 + 7771771 D-number 15 33 111 + 3313131 d-powerful 24 132 135 + 9983232 de Polignac 39393 71575 155575 + 97799373 decagonal 126 175 2232 + 491741712 deceptive 7777 11111 1111111 deficient 11 15 22 + 9999999 dig.balanced 11 12 15 + 199996128 double fact. 15 48 384 135135 droll 672 4224 48384 + 4214784 Duffinian 36 55 77 + 9977373 eban 36 44 66 economical 11 15 111 + 19999791 emirpimes 15 115 122 + 17177111 enlightened 2744 23328 236196 equidigital 11 15 111 + 19999791 eRAP 24 1198224 26642688 + 472113432 esthetic 12 212 432 + 434343432 Eulerian 11 66 evil 12 15 24 + 499999824 factorial 24 fibodiv 122 244 366 + 114912936 Fibonacci 55 144 46368 Friedman 126 128 216 + 983664 frugal 128 1715 11664 + 499213368 gapful 132 135 264 + 499999968 Giuga 1722 good prime 11 happy 44 784 888 + 9999864 harmonic 672 8128 32997888 Harshad 12 24 36 + 499999968 heptagonal 55 112 1288 + 494469144 hex 1771777 hexagonal 15 66 1128 + 481228776 highly composite 12 24 36 48 hoax 22 336 424 + 99991332 Hogben 111 house 155 1288848 13413636 hungry 144 hyperperfect 8128 iban 11 12 22 + 777777 iccanobiF 124 idoneal 12 15 22 + 1848 impolite 128 inconsummate 216 432 488 + 999936 insolite 111 11112 1122112 + 122121216 interprime 12 15 99 + 99999936 Jacobsthal 11 Jordan-Polya 12 24 36 + 429981696 junction 111 115 212 + 99999162 Kaprekar 55 99 999 + 432432432 katadrome 432 864 6432 + 9864 Lehmer 15 1111 11155 + 771715 Leyland 1124 93312 94932 lonely 1344 Lucas 11 lucky 15 33 99 + 9991395 Lynch-Bell 12 15 24 + 9867312 magic 15 111 175 + 336111126 magnanimous 11 12 112 + 111112 metadrome 12 15 24 + 1368 modest 111 222 333 + 496867896 Moran 111 222 333 + 99919926 nialpdrome 11 22 33 + 444444444 nonagonal 24 111 396 + 499946184 O'Halloran 12 36 44 oban 11 12 15 + 999 octagonal 936 3816 6816 + 499668696 odious 11 22 44 + 499999968 palindromic 11 22 33 + 489939984 palprime 11 pancake 11 22 1771 + 22221112 panconsummate 11 12 15 + 144 pandigital 11 15 99 + 379772316 partition 11 15 22 + 8118264 pentagonal 12 22 1335 + 444164292 perfect 8128 pernicious 11 12 22 + 9999288 Perrin 12 22 plaindrome 11 12 15 + 488888888 power 36 128 144 + 494439696 powerful 36 128 144 + 498389976 practical 12 24 36 + 9999936 prim.abundant 12 66 88 + 88828144 prime 11 pronic 12 132 1122 + 482614992 Proth 33 3393 319717377 pseudoperfect 12 24 36 + 999999 repdigit 11 22 33 + 444444444 repunit 15 111 1111 + 118612344 Ruth-Aaron 15 24 77 + 491614236 Sastry 13224 self 132 222 244 + 499999932 self-describing 22 4444 224444 + 88888888 semiprime 15 22 33 + 77717171 sliding 11 Smith 22 636 648 + 99993492 Sophie Germain 11 sphenic 66 222 366 + 77777133 square 36 144 324 + 494439696 straight-line 111 135 222 + 444444444 strobogrammatic 11 88 111 + 111111111 strong prime 11 subfactorial 44 super Niven 12 24 36 48 super-d 333 336 784 + 9999666 superabundant 12 24 36 48 tau 12 24 36 + 499999968 taxicab 32832 39312 314496 + 482831496 tetrahedral 816 1771 3276 + 12614424 tetranacci 15 triangular 15 36 55 + 488234376 tribonacci 24 44 trimorphic 24 99 624 + 99999999 twin 11 uban 11 12 15 + 99 Ulam 11 36 48 + 9999999 undulating 212 424 515 + 424242424 unprimeable 324 515 624 + 9999648 untouchable 88 124 162 + 999396 upside-down 55 555 2288 + 55555555 vampire 1395 163944 186624 + 61612992 wasteful 12 22 24 + 9999999 Zuckerman 11 12 15 + 498161664 Zumkeller 12 24 48 + 99936 zygodrome 11 22 33 + 449996688