cp's OEIS Frontend

A285271 Numbers that are divisible by each of their digits but that are either not divisible by the sum of their digits or are not divisible by the product of their digits or both.

%I A285271 #66 May 04 2025 13:56:15
%S A285271 11,15,22,33,44,48,55,66,77,88,99,115,122,124,126,128,155,162,168,175,
%T A285271 184,212,222,244,248,264,288,324,333,336,366,384,396,412,424,444,448,
%U A285271 488,515,555,636,648,666,672,728,777,784,816,824,848,864,888,936,999,1111,1112
%N A285271 Numbers that are divisible by each of their digits but that are either not divisible by the sum of their digits or are not divisible by the product of their digits or both.
%C A285271 Numbers which are divisible by the sum and the product of their digits (A038186) are also divisible by each of their digits (A034838)
%C A285271 The product of the digits of n are trivially divisible by each digit; so if that product divides n, each digit must divide n. - _Franklin T. Adams-Watters_, Jul 02 2017
%H A285271 Robert G. Wilson v, <a href="/A285271/b285271.txt">Table of n, a(n) for n = 1..1520</a>
%e A285271 15 is divisible by its digits 1 and 5, and 15 is divisible by the product of its digits 1*5 = 5, but 15 is not divisible by the sum of its digits 1+5 = 6, hence 15 is a term.
%e A285271 48 is divisible by its digits 4 and 8, and 48 is divisible by the sum of its digits 4+8 = 12, but 48 is not divisible by the product of its digits 4*8 = 32, hence 48 is a term.
%e A285271 124 is divisible by its digits 1, 2 and 4, but 124 is not divisible by the product of its digits 1*2*4 = 8 and 124 is not divisible by the sum of its digits 1+2+4 = 7, hence 124 is a term.
%e A285271 24 is divisible by its digits 2 and 4, and 24 is divisible by the sum of its digits 2+4 = 6, and 24 is also divisible by the product of its digits 2*4 = 8, hence 24 is NOT a term.
%p A285271 filter:= proc(n) local F;
%p A285271    F:= convert(n,base,10);
%p A285271    andmap(t -> t > 0 and n mod t = 0, F) and not(n mod convert(F,`+`) = 0 and n mod convert(F,`*`) = 0)
%p A285271 end proc:
%p A285271 select(filter, [$11 .. 2000]); # _Robert Israel_, Jul 05 2017
%t A285271 fQ[n_] := Block[{ind = IntegerDigits@ n}, Union[ IntegerQ@# & /@ (n/ind)] == {True} && (!IntegerQ[n/Plus @@ ind] || !IntegerQ[n/Times @@ ind])]; Select[Range@ 1112, fQ] (* _Robert G. Wilson v_, Jul 05 2017 *)
%t A285271 nddQ[n_]:=With[{idn=IntegerDigits[n]},FreeQ[idn,0]&&AllTrue[n/idn,IntegerQ]&&(!IntegerQ[n/Times@@idn]||!IntegerQ[n/Total[idn]])]; Select[Range[1200],nddQ] (* _Harvey P. Dale_, May 04 2025 *)
%o A285271 (PARI) isok(n) = {d = digits(n); if (vecmin(d), for (k=1, #d, if (n % d[k], return (0));); return ((n % vecsum(d)) || (n % prod(k=1, #d, d[k])));); return (0);} \\ _Michel Marcus_, Jul 02 2017
%Y A285271 Subsequence of A034838.
%Y A285271 Cf. A005349, A007602, A038186.
%K A285271 nonn,base
%O A285271 1,1
%A A285271 _Bernard Schott_, Jun 24 2017
%E A285271 Definition clarified by _Harvey P. Dale_, May 04 2025