cp's OEIS Frontend

A387159 Odd numbers k such that A173557(k) = A173557(sigma(k)), where A173557(n) is multiplicative with a(p^e) = p-1 and sigma is the sum of divisors function.

%I A387159 #12 Aug 20 2025 10:48:54
%S A387159 1,63,135,351,875,891,999,1647,1859,1971,4239,5211,7479,8451,10719,
%T A387159 11367,12339,14607,16317,16551,17847,18171,19791,20439,22103,23679,
%U A387159 26919,27951,29511,31131,31407,31487,32427,32751,33399,35667,37287,39231,43767,44739,47331,50571,52191,53811,54459,57319,57699,63207,66771
%N A387159 Odd numbers k such that A173557(k) = A173557(sigma(k)), where A173557(n) is multiplicative with a(p^e) = p-1 and sigma is the sum of divisors function.
%C A387159 Odd numbers k for which A173557(k) == A387157(k).
%H A387159 Antti Karttunen, <a href="/A387159/b387159.txt">Table of n, a(n) for n = 1..10000</a>
%H A387159 <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%H A387159 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A387159 A387159Q[k_] := OddQ[k] && #[k] == #[DivisorSigma[1, k]] & [Times @@ (FactorInteger[#][[All, 1]] - 1) &];
%t A387159 Select[Range[100000], A387159Q] (* _Paolo Xausa_, Aug 20 2025 *)
%o A387159 (PARI)
%o A387159 A173557(n) = factorback(apply(p -> p-1,factor(n)[,1]));
%o A387159 is_A387159(n) = (n%2 && (A173557(sigma(n))==A173557(n)));
%Y A387159 Odd terms of A387158.
%Y A387159 Cf. A000203, A173557, A387157.
%Y A387159 Cf. also A351443, A353679, A386425.
%K A387159 nonn
%O A387159 1,2
%A A387159 _Antti Karttunen_, Aug 19 2025