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A387157 a(n) = A173557(sigma(n)), where A173557(n) is multiplicative with a(p^e) = p-1 and sigma is the sum of divisors function.

%I A387157 #14 Aug 20 2025 10:56:01
%S A387157 1,2,1,6,2,2,1,8,12,2,2,6,6,2,2,30,2,24,4,12,1,2,2,8,30,12,4,6,8,2,1,
%T A387157 12,2,2,2,72,18,8,6,8,12,2,10,12,24,2,2,30,36,60,2,6,2,8,2,8,4,8,8,12,
%U A387157 30,2,12,126,12,2,16,12,2,2,2,96,36,36,30,24,2,12,4,60,10,12,12,6,2,20,8,8,8,24,6,12,1,2,8
%N A387157 a(n) = A173557(sigma(n)), where A173557(n) is multiplicative with a(p^e) = p-1 and sigma is the sum of divisors function.
%H A387157 Antti Karttunen, <a href="/A387157/b387157.txt">Table of n, a(n) for n = 1..10000</a>
%F A387157 a(n) = A003958(A080398(n)).
%t A387157 A387157[n_] := If[n == 1, 1, Times @@ (FactorInteger[DivisorSigma[1, n]][[All, 1]] - 1)];
%t A387157 Array[A387157, 100] (* _Paolo Xausa_, Aug 20 2025 *)
%o A387157 (PARI) A387157(n) = factorback(apply(p -> p-1,factor(sigma(n))[,1]));
%Y A387157 Cf. A000203, A003958, A080398, A173557, A387158 (positions where equal to A173557(n)).
%Y A387157 Cf. also A351442.
%K A387157 nonn,new
%O A387157 1,2
%A A387157 _Antti Karttunen_, Aug 19 2025