A298754 -id:A298754 - cp's OEIS frontend

A091260 Denominator of sigma_3(n)/sigma_2(n).

1, 5, 5, 21, 13, 25, 25, 17, 91, 65, 61, 15, 85, 125, 65, 11, 145, 455, 181, 13, 125, 305, 265, 85, 651, 425, 41, 525, 421, 325, 481, 455, 305, 725, 325, 1911, 685, 181, 425, 17, 841, 625, 925, 427, 169, 1325, 1105, 55, 817, 1085, 725, 255, 1405, 205, 793, 425, 181

Offset: 1

Labos Elemer, Feb 12 2004

If n is an odd prime then a(n) = A001844((n-1)/2). - Robert Israel, Jan 26 2018

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001158, A001157, A000203, A091258, A091259, A298754 (numerator), A001844.

seq(denom(numtheory:-sigma[3](n)/numtheory:-sigma[2](n)),n=1..100); # Robert Israel, Jan 26 2018

Denominator[Table[DivisorSigma[3,n]/DivisorSigma[2,n],{n,60}]] (* Harvey P. Dale, Nov 03 2011 *)

a(n) = my(f = factor(n)); denominator(sigma(f, 3)/sigma(f, 2)); \\ Amiram Eldar, Dec 20 2024

A379814 a(n) = sigma_2(n) * sigma_3(n).

Original entry on oeis.org

1, 45, 280, 1533, 3276, 12600, 17200, 49725, 68887, 147420, 162504, 429240, 373660, 774000, 917280, 1596221, 1425060, 3099915, 2483320, 5022108, 4816000, 7312680, 6449040, 13923000, 10253901, 16814700, 16760800, 26367600, 20536380, 41277600, 28659904, 51117885

Offset: 1

Amiram Eldar, Jan 03 2025

See A379812 for more links and Ramanujan's general formula.

Srinivasa Ramanujan, Collected papers, edited by G. H. Hardy et al., Chelsea, 1962, chapter 17, pp. 133-135.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Srinivasa Ramanujan, Some formulae in the analytic theory of numbers, Messenger of Mathematics, Vol. 45 (1916), pp. 81-84.

Cf. A001157, A001158, A091260, A092344, A092344, A298754, A379812, A379813.

Cf. A002117, A013662, A013664, A013665.

a[n_] := Times @@ DivisorSigma[{2, 3}, n]; Array[a, 50]

a(n) = {my(f = factor(n)); sigma(f, 2) * sigma(f, 3);}

a(n) = A001157(n) * A001158(n).
Multiplicative with a(p^e) = (p^(2*e+2)-1) * (p^(3*e+3)-1) / ((p^2-1) * (p^3-1)).
Dirichlet g.f.: zeta(s) * zeta(s-2) * zeta(s-3) * zeta(s-5) / zeta(2*s-5).
Sum_{k=1..n}  a(k) ~ c * n^6 / 6, where c = zeta(3) * zeta(4) * zeta(6) / zeta(7) = Pi^10 * zeta(3) / (85050 * zeta(7)) = 1.31261826893951336264... .

cp's OEIS Frontend

A091260 Denominator of sigma_3(n)/sigma_2(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI