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.

1, 6, 26, 28, 63, 74, 120, 122, 135, 146, 270, 314, 351, 386, 416, 496, 520, 554, 626, 672, 794, 842, 875, 891, 914, 999, 1080, 1082, 1226, 1232, 1322, 1346, 1404, 1466, 1480, 1514, 1638, 1647, 1750, 1754, 1782, 1859, 1971, 1994, 2186, 2306, 2402, 2426, 2440, 2474, 2642, 2762, 2906, 2920, 3242, 3314, 3506, 3718

Offset: 1

Author

Antti Karttunen, Aug 19 2025

Keywords

• nonn
• new

Comments

Numbers k for which A173557(k) == A387157(k).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences where odd perfect numbers must occur, if they exist at all
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A173557, A387157.

Subsequences: A000396, A387159 (odd terms).

Cf. also A006872, A351446, A386424.

Programs

Mathematica

A387158Q[k_] := #[k] == #[DivisorSigma[1, k]] & [Times @@ (FactorInteger[#][[All, 1]] - 1) &];
Select[Range[10000], A387158Q] (* Paolo Xausa, Aug 20 2025 *)

PARI

A173557(n) = factorback(apply(p -> p-1,factor(n)[,1]));
is_A387158(n) = (A173557(sigma(n))==A173557(n));