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A379928 Numbers m such that A379742(m) is a multiple of A027423(m).

%I A379928 #23 Jan 16 2025 02:39:06
%S A379928 0,1,2,10,17,26,30,36,43,57,58,67,73,74,82,99,103,105,114,125,129,138,
%T A379928 147,161,165,173,186,194,201,237,239,261,269,275,291,299,314,315,317,
%U A379928 345,347,375,377,381,383,387,402,411,413,437,447,458,467,485,495,506,513,515,519
%N A379928 Numbers m such that A379742(m) is a multiple of A027423(m).
%C A379928 Apparently, almost all the terms are odd (asymptotically). Among the first 10^4 terms there are only 43 even terms, and only 2 of them, 0 and 36, are divisible by 4. - _Amiram Eldar_, Jan 15 2025
%H A379928 Amiram Eldar, <a href="/A379928/b379928.txt">Table of n, a(n) for n = 1..10000</a> (terms 2..114 from Michel Marcus)
%t A379928 Select[Range[0, 520], Divisible @@ DivisorSigma[0, {BarnesG[# + 2], #!}] &] (* _Amiram Eldar_, Jan 06 2025 *)
%o A379928 (PARI) isok(m) = numdiv(prod(k=1, m, k!)) % numdiv(m!) == 0;
%o A379928 (PARI) isok(m) = {my(prd = 1); forprime(p = 2, m, prd *= ((1 + (m*(m+1)/2 - 1 - sum(i = 2, m, sumdigits(i, p)))/(p-1)) / (1 + (m - sumdigits(m, p))/(p-1)))); denominator(prd) == 1;} \\ _Amiram Eldar_, Jan 15 2025
%Y A379928 Cf. A000142, A000178, A027423, A379742.
%K A379928 nonn
%O A379928 1,3
%A A379928 _Michel Marcus_, Jan 06 2025
%E A379928 a(1) = 0 inserted by _Amiram Eldar_, Jan 15 2025