OFFSET
1,2
COMMENTS
Inspired by A333456.
A Zuckerman number (A007602) is a number that is divisible by the product of its digits; e.g., 24 is a Zuckerman number because it is divisible by 2*4=8.
The divisors 1 and m (if m is itself a Zuckerman number) are included.
Conjecture: m always exists.
Not all terms in the sequence are Zuckerman numbers. For example a(7) = 84 has product of digits = 32 and 84/32 = 21/8 = 2.625.
LINKS
Giovanni Resta, Zuckerman numbers, Numbers Aplenty.
EXAMPLE
Of the six divisors of 18, five are Zuckerman numbers: 1, 2, 3, 6 and 9, and there is no smaller number with five Zuckerman divisors, hence a(5) = 18.
MATHEMATICA
zuckQ[n_] := (prodig = Times @@ IntegerDigits[n]) > 0 && Divisible[n, prodig]; numDiv[n_] := Count[Divisors[n], _?(zuckQ[#] &)]; mx = 50; n = 1; c = 0; v = Table[0, {mx}]; While[c < mx, i = numDiv[n]; If[i <= mx && v[[i]] == 0, c++; v[[i]] = n]; n++]; v (* Amiram Eldar, Jun 03 2020 *)
PROG
(PARI) iszu(n) = my(p=vecprod(digits(n))); p && !(n % p);
a(n) = {my(k=1); while (sumdiv(k, d, iszu(d)) !=n, k++); k; } \\ Michel Marcus, Jun 03 2020
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Jun 03 2020
EXTENSIONS
More terms from Amiram Eldar, Jun 03 2020
Edited, added escape clause. - N. J. A. Sloane, Jun 04 2020
STATUS
approved
