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%I #20 Oct 06 2020 06:19:29
%S 1,2,3,4,5,6,7,8,9,11,12,15,24,1111111111111111111,
%T 11111111111111111111111
%N Numbers whose divisors are all Zuckerman numbers (A007602).
%C Inspired by A337741.
%C Zuckerman numbers are numbers that are divisible by the product of their digits (see link).
%C The next term is the repunit prime R_317 which is too large to include in the data.
%C Primes in this sequence are 2, 3, 5, 7 and all the repunit primes (see A004023).
%C This sequence is infinite if and only if there are infinitely many repunit primes.
%H Giovanni Resta, <a href="http://www.numbersaplenty.com/set/Zuckerman_number/">Zuckerman numbers</a>, Numbers Aplenty
%e 6 is a term since all the divisors of 6, i.e., 1, 2, 3 and 6, are Zuckerman numbers.
%t zuckQ[n_] := (prod = Times @@ IntegerDigits[n]) > 0 && Divisible[n, prod]; Select[Range[24], AllTrue[Divisors[#], zuckQ] &] (* _Amiram Eldar_, Oct 01 2020 *)
%o (PARI) isok(m) = {fordiv(m, d, my(p=vecprod(digits(d))); if (!p || (d % p), return (0))); return (1);} \\ _Michel Marcus_, Oct 05 2020
%Y Subsequence of A007602.
%Y Similar sequences: A062687, A190217, A308851, A329419, A337741.
%Y Cf. A004023, A335037, A335038.
%Y Cf. A004022 (subsequence of prime repunits).
%K nonn,base
%O 1,2
%A _Bernard Schott_, Oct 01 2020
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