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A387158 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 A387158 #11 Aug 20 2025 10:48:42
%S A387158 1,6,26,28,63,74,120,122,135,146,270,314,351,386,416,496,520,554,626,
%T A387158 672,794,842,875,891,914,999,1080,1082,1226,1232,1322,1346,1404,1466,
%U A387158 1480,1514,1638,1647,1750,1754,1782,1859,1971,1994,2186,2306,2402,2426,2440,2474,2642,2762,2906,2920,3242,3314,3506,3718
%N A387158 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 A387158 Numbers k for which A173557(k) == A387157(k).
%H A387158 Antti Karttunen, <a href="/A387158/b387158.txt">Table of n, a(n) for n = 1..10000</a>
%H A387158 <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%H A387158 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A387158 A387158Q[k_] := #[k] == #[DivisorSigma[1, k]] & [Times @@ (FactorInteger[#][[All, 1]] - 1) &];
%t A387158 Select[Range[10000], A387158Q] (* _Paolo Xausa_, Aug 20 2025 *)
%o A387158 (PARI)
%o A387158 A173557(n) = factorback(apply(p -> p-1,factor(n)[,1]));
%o A387158 is_A387158(n) = (A173557(sigma(n))==A173557(n));
%Y A387158 Cf. A000203, A173557, A387157.
%Y A387158 Subsequences: A000396, A387159 (odd terms).
%Y A387158 Cf. also A006872, A351446, A386424.
%K A387158 nonn
%O A387158 1,2
%A A387158 _Antti Karttunen_, Aug 19 2025