A337163 -id:A337163 - cp's OEIS frontend

A087142 Numbers divisible by their individual digits, but not by the sum of their digits (counted with multiplicity).

11, 15, 22, 33, 44, 55, 66, 77, 88, 99, 115, 122, 124, 128, 155, 168, 175, 184, 212, 244, 248, 366, 384, 412, 424, 488, 515, 636, 672, 728, 784, 816, 824, 848, 1111, 1112, 1113, 1115, 1124, 1131, 1144, 1155, 1176, 1184, 1197, 1222, 1244, 1248, 1266, 1288, 1311

Offset: 1

Reinhard Zumkeller, Aug 18 2003

Intersection of A034838 and A065877.

			488 is in the sequence as its divisible by its individual digits but not by the sum of its digits counted with multiplicity. That is 488 is divisible by 4 and 8 but not by 4 + 8 + 8 = 20. - _David A. Corneth_, Jan 28 2021

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Cf. A034838, A052382, A065877, A087141.

Cf. A337163 (similar, with product).

didQ[n_]:=Module[{idn=IntegerDigits[n]},FreeQ[idn,0]&&AllTrue[n/idn, IntegerQ] && !Divisible[n,Total[idn]]]; Select[Range[1300], didQ] (* The program uses the AllTrue function from Mathematica version 10 *)  (* Harvey P. Dale, Apr 18 2016 *)

is(n) = { my(d = digits(n), sd = vecsum(d), s = Set(d)); if(n == 0 || s[1] == 0, return(0)); if(n % sd != 0, for(i = 1, #s, if(n % s[i] != 0, return(0) ) ); return(1) ); 0 } \\ David A. Corneth, Jan 28 2021

def ok(n):
    d = list(map(int, str(n)))
    return 0 not in d and n%sum(d) and all(n%di == 0 for di in set(d))
print([k for k in range(1312) if ok(k)]) # Michael S. Branicky, Nov 15 2021

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

Original entry on oeis.org

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

Bernard Schott, Mar 20 2021

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.

			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.

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

Equals A002796 \ A055471.

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

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 *)

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

cp's OEIS Frontend

A087142 Numbers divisible by their individual digits, but not by the sum of their digits (counted with multiplicity).

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