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A340638 Integers whose number of divisors that are Zuckerman numbers sets a new record.

%I A340638 #33 Jul 19 2021 01:23:40
%S A340638 1,2,4,6,12,24,72,144,360,432,1080,2016,2160,6048,8064,15120,24192,
%T A340638 48384,88704,120960,241920,266112,532224,1064448,1862784,2661120,
%U A340638 3725568,5322240,7451136,10450944,19160064,20901888,28740096,38320128,57480192,99283968,114960384
%N A340638 Integers whose number of divisors that are Zuckerman numbers sets a new record.
%C A340638 A Zuckerman number is a number that is divisible by the product of its digits (A007602).
%C A340638 The terms in this sequence are not necessarily Zuckerman numbers. For example a(7) = 72 has product of digits = 14 and 72/14 = 36/7 = 5.142...
%C A340638 The first seven terms are the first seven terms of A087997, then A087997(8) = 66 while a(8) = 144.
%H A340638 Giovanni Resta, <a href="http://www.numbersaplenty.com/set/Zuckerman_number/">Zuckerman numbers</a>, Numbers Aplenty.
%e A340638 The 8 divisors of 24 are all Zuckerman numbers, and also, 24 is the smallest integer that has at least 8 divisors that are Zuckerman numbers, hence 24 is a term.
%t A340638 zuckQ[n_] := (prod = Times @@ IntegerDigits[n]) > 0 && Divisible[n, prod]; s[n_] := DivisorSum[n, 1 &, zuckQ[#] &]; smax = 0; seq = {}; Do[s1 = s[n]; If[s1 > smax, smax = s1; AppendTo[seq, n]], {n, 1, 10^5}]; seq (* _Amiram Eldar_, Jan 14 2021 *)
%o A340638 (PARI) isokz(n) = iferr(!(n % vecprod(digits(n))), E, 0); \\ A007602
%o A340638 lista(nn) = {my(m=0); for (n=1, nn, my(x = sumdiv(n, d, isokz(d));); if (x > m, m = x; print1(n, ", ")););} \\ _Michel Marcus_, Jan 15 2021
%Y A340638 Cf. A007602, A335037, A337941.
%Y A340638 Subsequence of A335038.
%Y A340638 Similar for palindromes (A093036), repdigits (A340548), repunits (A340549), Niven numbers (A340637).
%K A340638 nonn,base
%O A340638 1,2
%A A340638 _Bernard Schott_, Jan 14 2021
%E A340638 More terms from _David A. Corneth_ and _Amiram Eldar_, Jan 15 2021