A091259 Numerator of sigma_3(n)/sigma(n).

1, 3, 7, 73, 21, 21, 43, 39, 757, 63, 111, 73, 157, 129, 147, 151, 273, 2271, 343, 219, 301, 333, 507, 273, 15751, 471, 511, 3139, 813, 441, 931, 4161, 777, 819, 903, 55261, 1333, 1029, 1099, 819, 1641, 903, 1807, 8103, 15897, 1521, 2163, 1057, 39331, 47253

Offset: 1

Author

Labos Elemer, Feb 12 2004

Keywords

• easy
• nonn
• frac
• look

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001158, A000203, A002061, A002117, A086463, A091258 (denominators), A091260.

Cf. A032766.

Programs

Magma

[Numerator(DivisorSigma(3,n)/DivisorSigma(1,n)): n in [1..50]]; // Vincenzo Librandi, Jan 26 2018

Maple

seq(numer(numtheory:-sigma[3](n)/numtheory:-sigma(n)),n=1..100); # Robert Israel, Jan 25 2018

Mathematica

Array[Numerator[DivisorSigma[3,#]/DivisorSigma[1,#]]&,50] (* Harvey P. Dale, Feb 29 2016 *)

PARI

a(n) = numerator(sigma(n, 3)/sigma(n)); \\ Michel Marcus, Jan 26 2018

Formula

a(p) = A002061(p), for prime p. - Robert Israel, Jan 25 2018

Sum_{k=1..n} a(k)/A091258(k) ~ c * n^3, where c = (Pi^2/18)*zeta(3)^2 * Product_{p prime} (1 - 2/p^2 - 1/p^3 + 5/p^5 - 3/p^6) = 0.2382648075... . - Amiram Eldar, Nov 21 2022

Conjecture: a(n) (mod 3) = A353816(n). - Michel Marcus, Aug 11 2024