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

1,2

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.

Links

Table of n, a(n) for n=1..15.

Giovanni Resta, Zuckerman numbers, Numbers Aplenty

Example

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

Mathematica

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

Prog

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

Crossrefs

Subsequence of A007602.

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

Cf. A004023, A335037, A335038.

Cf. A004022 (subsequence of prime repunits).

Sequence in context: A180484 A007602 A343681 * A167620 A169935 A193498

Adjacent sequences: A337938 A337939 A337940 * A337942 A337943 A337944

Keyword

nonn,base

Author

Bernard Schott, Oct 01 2020

Status

approved