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A351807 Integers m such that pod(m) divides pod(m^2) where pod = product of digits = A007954.

%I A351807 #30 Feb 20 2022 17:17:21
%S A351807 1,2,3,5,6,8,11,12,13,15,16,18,19,21,22,23,25,26,27,28,31,32,33,36,41,
%T A351807 42,43,45,47,48,49,51,52,53,55,61,62,63,64,66,68,71,74,76,78,82,83,84,
%U A351807 93,94,95,96,97,98,99,111,112,113,114,115,116,118,121,122,123
%N A351807 Integers m such that pod(m) divides pod(m^2) where pod = product of digits = A007954.
%C A351807 Inspired by A351650 where pod is replaced by sod.
%C A351807 All terms are zeroless (A052382).
%C A351807 Repunits form a subsequence (A002275).
%C A351807 Integers m without 0 and such that m^2 has a 0 form a subsequence (A134844).
%C A351807 The smallest term k such that the corresponding quotient = n is A351809(n).
%e A351807 Product of digits of 27 = 2*7 = 14; then 27^2 = 729, product of digits of 729 = 7*2*9 = 81; as 81 divides 729, 27 is a term.
%t A351807 pod[n_] := Times @@ IntegerDigits[n]; Select[Range[120], FreeQ[IntegerDigits[#], 0] && Divisible[pod[#^2], pod[#]] &] (* _Amiram Eldar_, Feb 19 2022 *)
%o A351807 (Python)
%o A351807 from math import prod
%o A351807 def pod(n): return prod(map(int, str(n)))
%o A351807 def ok(m): pdm = pod(m); return pdm > 0 and pod(m*m)%pdm == 0
%o A351807 print([m for m in range(124) if ok(m)]) # _Michael S. Branicky_, Feb 19 2022
%o A351807 (PARI) isok(m) = my(d=digits(m)); vecmin(d) && denominator(vecprod(digits(m^2))/vecprod(d)) == 1; \\ _Michel Marcus_, Feb 19 2022
%Y A351807 Cf. A007954, A002473, A351808 (corresponding quotients), A351809.
%Y A351807 Subsequences: A002275, A134844.
%K A351807 nonn,base
%O A351807 1,2
%A A351807 _Bernard Schott_, Feb 19 2022
%E A351807 More terms from _Amiram Eldar_, Feb 19 2022