cp's OEIS Frontend

A382402 Numbers divisible by the product of their digits (mod 10).

%I A382402 #19 Jun 02 2025 08:29:19
%S A382402 1,2,3,4,5,6,7,8,9,11,12,15,24,26,34,35,37,48,55,62,64,66,72,73,75,76,
%T A382402 78,84,88,95,96,98,99,111,112,115,126,132,134,135,136,137,144,148,155,
%U A382402 162,164,168,172,173,175,176,184,188,192,195,196,198,199,212,216,228,232,244,248,264,266
%N A382402 Numbers divisible by the product of their digits (mod 10).
%C A382402 Unlike A007602 and A064700, where there are no other primes besides 2, 3, 5, 7 and primes with repunits, this sequence contains other primes such as 37, 73 and 137.
%C A382402 The sequence has asymptotic density 0, since it contains no numbers with digit 5 and an even digit. - _Robert Israel_, Jun 01 2025
%H A382402 Robert Israel, <a href="/A382402/b382402.txt">Table of n, a(n) for n = 1..10000</a>
%p A382402 filter:= proc(n) local L,t;
%p A382402   L:= convert(n,base,10);
%p A382402   t:= convert(L,`*`) mod 10;
%p A382402   t > 0 and n mod t = 0
%p A382402 end proc:
%p A382402 select(filter, [$1..1000]); # _Robert Israel_, Jun 01 2025
%t A382402 Select[Range[300], (prod = Mod[Times @@ IntegerDigits[#], 10]) > 0 && Divisible[#, prod] &] (* _Amiram Eldar_, Mar 23 2025 *)
%o A382402 (Python)
%o A382402 from math import prod
%o A382402 def ok(n): return (p:=prod(map(int, str(n)))%10) > 0 and n%p == 0
%o A382402 print([k for k in range(300) if ok(k)]) # _Michael S. Branicky_, Mar 23 2025
%o A382402 (PARI) isok(k) = my(p=lift(vecprod(apply(x->Mod(x, 10), digits(k))))); if (p, !(k % p)); \\ _Michel Marcus_, Mar 31 2025
%Y A382402 Cf. A007602, A064700, A371281.
%K A382402 nonn,base
%O A382402 1,2
%A A382402 _Enrique Navarrete_, Mar 23 2025