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 A337941 Numbers whose divisors are all Zuckerman numbers (A007602). 1
 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 24, 1111111111111111111, 11111111111111111111111 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified September 23 02:41 EDT 2021. Contains 347609 sequences. (Running on oeis4.)