A387726 Powerful part of the sum of divisors of n: a(n) = A057521(A000203(n)).

1, 1, 4, 1, 1, 4, 8, 1, 1, 9, 4, 4, 1, 8, 8, 1, 9, 1, 4, 1, 32, 36, 8, 4, 1, 1, 8, 8, 1, 72, 32, 9, 16, 27, 16, 1, 1, 4, 8, 9, 1, 32, 4, 4, 1, 72, 16, 4, 1, 1, 72, 49, 27, 8, 72, 8, 16, 9, 4, 8, 1, 32, 8, 1, 4, 144, 4, 9, 32, 144, 72, 1, 1, 1, 4, 4, 32, 8, 16, 1, 121, 9, 4, 32, 108, 4, 8, 36, 9, 9, 16, 8, 128, 144

Offset

1,3

Links

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

Index entries for sequences related to sigma(n).

Formula

a(n) = A064549(A387156(n)).

Mathematica

A387726[n_] := Times @@ Power @@@ Select[FactorInteger[DivisorSigma[1, n]], Last[#] > 1 &];
Array[A387726, 100] (* Paolo Xausa, Sep 12 2025 *)

Prog

(PARI)
A057521(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1)); };
A387726(n) = A057521(sigma(n));

Crossrefs

Cf. A000203, A057521, A064549, A386424, A387156, A387727, A387728.

Sequence in context: A116669 A016523 A026998 * A326812 A324893 A301626

Adjacent sequences: A387723 A387724 A387725 * A387727 A387728 A387729

Keyword

nonn

Author

Antti Karttunen, Sep 12 2025

Status

approved