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%I #15 Apr 28 2021 06:04:14
%S 1,2,3,4,5,6,7,8,9,12,15,24,36,111,128,135,144,175,216,315,384,432,
%T 672,735,1296,1575,2916,11115,11232,11664,12132,12288,12312,13212,
%U 13824,14112,16416,22176,23112,23328,26112,27216,31212,32832,34272,34992,42624,72128,77175
%N Zuckerman numbers which when divided by the product of their digits, give a quotient which is a Niven (Harshad) number.
%C Repunit R(k) is a term iff k divides R(k) (A014950).
%H Giovanni Resta, <a href="https://www.numbersaplenty.com/set/Zuckerman_number/">Zuckerman numbers</a>, Numbers Aplenty.
%e 36 is a Zuckerman number as 36/(3*6) = 2, 2/2 = 1 that is a Niven number, and 36 is a term.
%e 315 is a Zuckerman number as 315/(3*1*5) = 21, 21/(2+1) = 7 that is a Niven number, and 315 is a term.
%t nivenQ[n_] := IntegerQ[n] && (sum = Plus @@ IntegerDigits[n]) > 0 && Divisible[n, sum]; Select[Range[10^5], (prod = Times @@ IntegerDigits[#]) > 0 && nivenQ[# / prod] &] (* _Amiram Eldar_, Apr 26 2021 *)
%o (PARI) isn(n) = !(n%sumdigits(n)); \\ A005349
%o isz(n) = my(p=vecprod(digits(n))); p && !(n % p); \\ A007602
%o isok(n) = isz(n) && isn(n/vecprod(digits(n))); \\ _Michel Marcus_, Apr 26 2021
%Y Cf. A005349, A007602, A235507, A288069, A343680, A343681.
%K nonn,base
%O 1,2
%A _Bernard Schott_, Apr 26 2021
%E More terms from _Michel Marcus_, Apr 26 2021
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