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
KEYWORD
mult,nonn
AUTHOR
Vladeta Jovovic, Oct 25 2001
STATUS
approved