A064840 a(n) = tau(n)*sigma(n).

1, 6, 8, 21, 12, 48, 16, 60, 39, 72, 24, 168, 28, 96, 96, 155, 36, 234, 40, 252, 128, 144, 48, 480, 93, 168, 160, 336, 60, 576, 64, 378, 192, 216, 192, 819, 76, 240, 224, 720, 84, 768, 88, 504, 468, 288, 96, 1240, 171, 558, 288, 588, 108, 960, 288, 960, 320, 360

Offset

1,2

Comments

Dirichlet convolution of A034761 with (the Dirichlet inverse of A037213). - R. J. Mathar, Feb 11 2011

Links

Indranil Ghosh, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)

Vaclav Kotesovec, Graph - the asymptotic ratio

Formula

Multiplicative with a(p^e) = (p^(e+1)-1)*(e+1)/(p-1). a(n) = (1/2)*Sum_{i|n, j|n} (i+j).

Dirichlet g.f. (zeta(s)*zeta(s-1))^2/zeta(2s-1). - R. J. Mathar, Feb 11 2011

Sum_{k=1..n} a(k) ~ Pi^4 * n^2 / (144*Zeta(3)) * (2*log(n) - 1 + 4*gamma - 4*Zeta'(3)/Zeta(3) + 24*Zeta'(2)/Pi^2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jan 31 2019

Example

For n = 10, a(10) = sigma(10) * tau(10) = 18 * 4 = 72. - Indranil Ghosh, Jan 20 2017

Maple

with(numtheory): seq(sigma(n)*tau(n), n=1..58) ; # Zerinvary Lajos, Jun 04 2008

Mathematica

Table[ DivisorSigma[0, n] * DivisorSigma[1, n], {n, 1, 58}] (* Jean-François Alcover, Mar 26 2013 *)

Prog

(Magma) [ NumberOfDivisors(n)*SumOfDivisors(n) : n in [1..40]];
(PARI) { for (n=1, 1000, a=numdiv(n)*sigma(n); write("b064840.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 28 2009

Crossrefs

Cf. A000005, A000203, A007503, A062354, A062355.

Sequence in context: A159469 A096524 A083595 * A306379 A243932 A242504

Adjacent sequences: A064837 A064838 A064839 * A064841 A064842 A064843

Keyword

mult,nonn

Author

Vladeta Jovovic, Oct 25 2001

Status

approved