A337163 Numbers divisible by their individual digits, but not by the product of their digits.

22, 33, 44, 48, 55, 66, 77, 88, 99, 122, 124, 126, 155, 162, 168, 184, 222, 244, 248, 264, 288, 324, 333, 336, 366, 396, 412, 424, 444, 448, 488, 515, 555, 636, 648, 666, 728, 777, 784, 824, 848, 864, 888, 936, 999, 1122, 1124, 1128, 1144, 1155, 1164, 1222

Offset: 1

Author

Bernard Schott, Jan 28 2021

Keywords

• nonn
• base

Comments

The sequence is infinite. For example, all numbers of the form ((10^n-1)/9)*(10^2)+24 are terms for n > 0. The numbers of this form will never be divisible by 8 but they will always be divisible by 1, 2 and 4. Also there are infinitely many terms any three of whose consecutive digits are distinct, for example, concatenations of 124. Are there infinitely many terms which don't consist of periodically repeating substrings? - Metin Sariyar, Jan 28 2021

Every repdigit non-repunit with at least 2 digits is a term. - Bernard Schott, Jan 28 2021

Examples

			48 is divisible by 4 and 8, but 48 is not divisible by 4*8 = 32, so 48 is a term.
128 is divisible by 1, 2 and 8, and 128 is divisible by 1*2*8 = 16 with 128 = 16*8, so 128 is not a term.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A034838 and A188643.

Cf. A087142 (similar, with sum).

Cf. A087141, A285271.

Programs

Mathematica

q[n_] := AllTrue[(digits = IntegerDigits[n]), # > 0 && Divisible[n, #] &] && !Divisible[n, Times @@ digits]; Select[Range[1000], q] (* Amiram Eldar, Jan 28 2021 *)

PARI

isok(n) = my(d=digits(n)); if (vecmin(d), for (i=1, #d, if (n % d[i], return(0))); (n % vecprod(d))); \\ Michel Marcus, Jan 28 2021

Extensions

More terms from Michel Marcus, Jan 28 2021