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

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, 78, 84, 88, 95, 96, 98, 99, 111, 112, 115, 126, 132, 134, 135, 136, 137, 144, 148, 155, 162, 164, 168, 172, 173, 175, 176, 184, 188, 192, 195, 196, 198, 199, 212, 216, 228, 232, 244, 248, 264, 266

Offset: 1

Author

Enrique Navarrete, Mar 23 2025

Keywords

• nonn
• base

Comments

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.

The sequence has asymptotic density 0, since it contains no numbers with digit 5 and an even digit. - Robert Israel, Jun 01 2025

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007602, A064700, A371281.

Programs

Maple

filter:= proc(n) local L,t;
  L:= convert(n,base,10);
  t:= convert(L,`*`) mod 10;
  t > 0 and n mod t = 0
end proc:
select(filter, [$1..1000]); # Robert Israel, Jun 01 2025

Mathematica

Select[Range[300], (prod = Mod[Times @@ IntegerDigits[#], 10]) > 0 && Divisible[#, prod] &] (* Amiram Eldar, Mar 23 2025 *)

PARI

isok(k) = my(p=lift(vecprod(apply(x->Mod(x, 10), digits(k))))); if (p, !(k % p)); \\ Michel Marcus, Mar 31 2025

Python

from math import prod
def ok(n): return (p:=prod(map(int, str(n)))%10) > 0 and n%p == 0
print([k for k in range(300) if ok(k)]) # Michael S. Branicky, Mar 23 2025