A342445 Numbers that are divisible by their nonzero digits but are not divisible by the product of their nonzero digits.

22, 33, 44, 48, 55, 66, 77, 88, 99, 122, 124, 126, 155, 162, 168, 184, 202, 204, 222, 244, 248, 264, 280, 288, 303, 324, 330, 333, 336, 366, 396, 404, 408, 412, 420, 424, 440, 444, 448, 488, 505, 515, 555, 606, 636, 648, 660, 666, 707, 728, 770, 777, 784, 808, 824, 840

Offset

1,1

Comments

Numbers that are divisible by the product of their nonzero digits (A055471) are trivially divisible by each of their nonzero digits (A002796), but the converse is false. This sequence = A002796 \ A055471 and consists of these counterexamples.

This sequence differs from A337163: the first sixteen terms are the same but a(17) = 202 while A337163(17) = 222.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..2000

Example

204 is divisible by 2 and 4 but 204 is not divisible by 2*4 = 8, hence 204 is a term.
248 is divisible by 2, by 4 and by 8 but 248 is not divisible by 2*4*8 = 64, hence 248 is a term.

Mathematica

q[n_] := AllTrue[(d = Select[IntegerDigits[n], # > 0 &]), Divisible[n, #] &] && ! Divisible[n, Times @@ d]; Select[Range[840], q] (* Amiram Eldar, Mar 21 2021 *)
dnzQ[n_]:=With[{c=DeleteCases[IntegerDigits[n], 0]}, Union[Boole[Divisible[n, c]]]=={1}&&!Divisible[n, Times@@c]]; Select[ Range[ 1000], dnzQ] (* Harvey P. Dale, Jan 16 2025 *)

Prog

(PARI) isok(m) = my(d=select(x->(x != 0), digits(m))); (m % vecprod(d)) && (sum(k=1, #d, m % d[k]) == 0); \\ Michel Marcus, Mar 22 2021

Crossrefs

Equals A002796 \ A055471.

Cf. A337163 = A034838 \ A007602 (subsequence of zeroless numbers).

Sequence in context: A084996 A250180 A252078 * A337163 A157496 A096768

Adjacent sequences: A342442 A342443 A342444 * A342446 A342447 A342448

Keyword

nonn,base

Author

Bernard Schott, Mar 20 2021

Status

approved