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%I #20 Apr 28 2021 06:11:26
%S 1,2,3,4,5,6,7,8,9,12,18,21,24,27,36,42,45,48,54,63,72,81,84,108,135,
%T 198,216,324,648,1008,1035,1050,1152,1215,1344,1380,1680,1725,2016,
%U 2376,2592,2625,2688,2997,3675,3816,3888,5616,5670,6912,10008,10017,10035,10044
%N Niven (or Harshad) numbers which when divided by sum of their digits, give a quotient which is a Zuckerman number.
%C The first 24 terms of A114440 are the first 24 terms of this sequence, then A114440(25) = 162, while a(25) = 135.
%H Giovanni Resta, <a href="https://www.numbersaplenty.com/set/Zuckerman_number/">Zuckerman Numbers</a>, Numbers Aplenty.
%e 84 is a Niven number as 84/(8+4) = 7, 7/7 = 1 so 7 is a Zuckerman number, and 84 is a term.
%e 108 is a Niven number as 108/(1+0+8) = 12, 12/(1*2) = 6 so 12 is a Zuckerman number, and 108 is a term.
%t zuckQ[n_] := IntegerQ[n] && (prod = Times @@ IntegerDigits[n]) > 0 && Divisible[n, prod]; Select[Range[10^4], zuckQ[#/Plus @@ IntegerDigits[#]] &] (* _Amiram Eldar_, Apr 26 2021 *)
%o (PARI) isz(n) = my(p=vecprod(digits(n))); p && !(n % p); \\ A007602
%o isok(n) = my(s=sumdigits(n)); !(n%s) && isz(n/s); \\ _Michel Marcus_, Apr 26 2021
%Y Cf. A005349, A007602, A114440, A235507.
%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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