A378995 Numerator of sigma(2*n)/(2*n).

3, 7, 2, 15, 9, 7, 12, 31, 13, 21, 18, 5, 21, 2, 12, 63, 27, 91, 30, 9, 16, 21, 36, 31, 93, 49, 20, 15, 45, 14, 48, 127, 24, 63, 72, 65, 57, 35, 28, 93, 63, 8, 66, 45, 13, 42, 72, 21, 171, 217, 36, 105, 81, 70, 108, 31, 40, 105, 90, 3, 93, 56, 52, 255, 126, 28, 102, 135, 48, 12, 108, 403, 111, 133, 62, 75, 144, 98, 120

Offset: 1

Author

Antti Karttunen, Dec 13 2024

Keywords

• nonn
• frac
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..32769
• Index entries for sequences related to sigma(n).

Crossrefs

Even bisection of A017665.

Topmost row of array A341605.

Cf. A062731, A245058, A378994, A378996 (denominators).

Cf. also A341525.

Programs

Mathematica

a[n_] := Numerator[DivisorSigma[-1, 2*n]]; Array[a, 100] (* Amiram Eldar, Dec 14 2024 *)

PARI

A378995(n) = numerator(sigma(2*n)/(2*n));

Formula

a(n) = A017665(2*n).

a(n) = A062731(n) / A378994(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A378996(k) = 5*Pi^2/24 (= 10 * A245058). - Amiram Eldar, Dec 14 2024