A387157 -id:A387157 - cp's OEIS frontend

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

Antti Karttunen, Aug 19 2025

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

Cf. A000203, A173557, A387157.
Subsequences: A000396, A387159 (odd terms).
Cf. also A006872, A351446, A386424.

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

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

A387156 a(n) = A003557(sigma(n)), where A003557(n) is multiplicative with a(p^e) = p^(e-1), and sigma is the sum of divisors function.

Original entry on oeis.org

1, 1, 2, 1, 1, 2, 4, 1, 1, 3, 2, 2, 1, 4, 4, 1, 3, 1, 2, 1, 16, 6, 4, 2, 1, 1, 4, 4, 1, 12, 16, 3, 8, 9, 8, 1, 1, 2, 4, 3, 1, 16, 2, 2, 1, 12, 8, 2, 1, 1, 12, 7, 9, 4, 12, 4, 8, 3, 2, 4, 1, 16, 4, 1, 2, 24, 2, 3, 16, 24, 12, 1, 1, 1, 2, 2, 16, 4, 8, 1, 11, 3, 2, 16, 18, 2, 4, 6, 3, 3, 8, 4, 64, 24, 4, 6, 7, 3, 2

Offset: 1

Antti Karttunen, Aug 19 2025

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000203, A003557, A062401, A080398, A387157.

Cf. also A386424, A386425.

A387156[n_] := # / Times @@ FactorInteger[#][[All, 1]] & [DivisorSigma[1, n]];
Array[A387156, 100] (* Paolo Xausa, Aug 20 2025 *)

A387156(n) = { my(s=sigma(n)); s/factorback(factor(s)[,1]); };

a(n) = A000203(n) / A080398(n).

a(n) = A062401(n) / A387157(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.

Original entry on oeis.org

1, 63, 135, 351, 875, 891, 999, 1647, 1859, 1971, 4239, 5211, 7479, 8451, 10719, 11367, 12339, 14607, 16317, 16551, 17847, 18171, 19791, 20439, 22103, 23679, 26919, 27951, 29511, 31131, 31407, 31487, 32427, 32751, 33399, 35667, 37287, 39231, 43767, 44739, 47331, 50571, 52191, 53811, 54459, 57319, 57699, 63207, 66771

Offset: 1

Antti Karttunen, Aug 19 2025

Odd numbers k for which A173557(k) == A387157(k).

Odd terms of A387158.
Cf. A000203, A173557, A387157.
Cf. also A351443, A353679, A386425.

A387159Q[k_] := OddQ[k] && #[k] == #[DivisorSigma[1, k]] & [Times @@ (FactorInteger[#][[All, 1]] - 1) &];
Select[Range[100000], A387159Q] (* Paolo Xausa, Aug 20 2025 *)

A173557(n) = factorback(apply(p -> p-1,factor(n)[,1]));
is_A387159(n) = (n%2 && (A173557(sigma(n))==A173557(n)));

cp's OEIS Frontend

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.

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A387156 a(n) = A003557(sigma(n)), where A003557(n) is multiplicative with a(p^e) = p^(e-1), and sigma is the sum of divisors function.

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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.

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