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A343681 Zuckerman numbers which when divided by product of their digits, give a quotient which is also a Zuckerman number.

%I A343681 #23 May 06 2022 13:13:51
%S A343681 1,2,3,4,5,6,7,8,9,11,12,15,24,36,111,128,135,144,175,384,672,735,
%T A343681 1111,1296,1575,11111,22176,42624,82944,111111,139968,688128,719712,
%U A343681 1111111,1161216,1492992,2241792,2794176,4136832,4741632,6838272,11111111,12171264,13395375,13436928
%N A343681 Zuckerman numbers which when divided by product of their digits, give a quotient which is also a Zuckerman number.
%C A343681 Alternative Name: Zuckerman numbers k such that k/(product of digits of k) is also a Zuckerman number. - _Wesley Ivan Hurt_, Apr 26 2021
%C A343681 All positive repunits are terms (A002275).
%H A343681 Giovanni Resta, <a href="/A343681/b343681.txt">Table of n, a(n) for n = 1..160</a> (terms < 3*10^14)
%H A343681 Giovanni Resta, <a href="https://www.numbersaplenty.com/set/Zuckerman_number/">Zuckerman numbers</a>, Numbers Aplenty.
%e A343681 24 is a Zuckerman number as 24/(2*4) = 3, 3/3 = 1 so 3 is also a Zuckerman number, and 24 is a term.
%e A343681 1296 is a Zuckerman number as 1296/(1*2*9*6) = 12, 12/(1*2) = 4 so 12 is also a Zuckerman number and 1296 is a term.
%t A343681 zuckQ[n_] := (prod = Times @@ IntegerDigits[n]) > 0 && Divisible[n, prod]; Select[Range[10^6], zuckQ[#] && zuckQ[#/Times @@ IntegerDigits[#]] &] (* _Amiram Eldar_, Apr 26 2021 *)
%o A343681 (PARI) isz(n) = my(p=vecprod(digits(n))); p && !(n % p); \\ A007602
%o A343681 isok(n) = isz(n) && isz(n/vecprod(digits(n))); \\ _Michel Marcus_, Apr 26 2021
%Y A343681 Cf. A002275, A007602, A288069, A343680, A343682.
%Y A343681 Cf. A235507 (similar, with Niven numbers).
%K A343681 nonn,base
%O A343681 1,2
%A A343681 _Bernard Schott_, Apr 26 2021
%E A343681 More terms from _David A. Corneth_, Apr 26 2021