OFFSET
1,2
COMMENTS
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
Logarithmic derivative of A174465.
Dirichlet g.f. zeta(s)*(zeta(s-1))^3. - R. J. Mathar, Feb 06 2011
a(n) = Sum_{d|n} tau_3(d)*d = Sum_{d|n} A007425(d)*d. - Enrique Pérez Herrero, Jan 17 2013
G.f.: Sum_{k>=1} k*tau_3(k)*x^k/(1 - x^k). - Ilya Gutkovskiy, Sep 06 2018
Sum_{k=1..n} a(k) ~ Pi^2*n^2/24 * (log(n)^2 + ((6*g - 1) + 12*z1/Pi^2) * log(n) + (1 - 6*g + 12*g^2 - 12*sg1)/2 + 6*((6*g - 1)*z1 + z2)/Pi^2), where g is the Euler-Mascheroni constant A001620, sg1 is the first Stieltjes constant A082633, z1 = Zeta'(2) = A073002, z2 = Zeta''(2) = A201994. - Vaclav Kotesovec, Feb 02 2019
PROG
(PARI) {a(n)=sumdiv(n, d, d*sigma(n/d)*sigma(d, 0))}
(Haskell)
a174466 n = sum $ zipWith3 (((*) .) . (*))
divs (map a000203 $ reverse divs) (map a000005 divs)
where divs = a027750_row n
-- Reinhard Zumkeller, Jan 21 2014
(Magma) [&+[d*DivisorSigma(1, n div d)*#Divisors(d):d in Divisors(n)]:n in [1..55]]; // Marius A. Burtea, Oct 18 2019
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Paul D. Hanna, Apr 04 2010
STATUS
approved