A337941 Numbers whose divisors are all Zuckerman numbers (A007602).

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 24, 1111111111111111111, 11111111111111111111111

Offset: 1

Author

Bernard Schott, Oct 01 2020

Keywords

• nonn
• base

Comments

Inspired by A337741.

Zuckerman numbers are numbers that are divisible by the product of their digits (see link).

The next term is the repunit prime R_317 which is too large to include in the data.

Primes in this sequence are 2, 3, 5, 7 and all the repunit primes (see A004023).

This sequence is infinite if and only if there are infinitely many repunit primes.

Examples

			6 is a term since all the divisors of 6, i.e., 1, 2, 3 and 6, are Zuckerman numbers.
		

Links

• Giovanni Resta, Zuckerman numbers, Numbers Aplenty

Crossrefs

Subsequence of A007602.

Similar sequences: A062687, A190217, A308851, A329419, A337741.

Cf. A004023, A335037, A335038.

Cf. A004022 (subsequence of prime repunits).

Programs

Mathematica

zuckQ[n_] := (prod = Times @@ IntegerDigits[n]) > 0 && Divisible[n, prod]; Select[Range[24], AllTrue[Divisors[#], zuckQ] &] (* Amiram Eldar, Oct 01 2020 *)

PARI

isok(m) = {fordiv(m, d, my(p=vecprod(digits(d))); if (!p || (d % p), return (0))); return (1);} \\ Michel Marcus, Oct 05 2020