OFFSET
1,2
LINKS
T. D. Noe, Table of n, a(n) for n=1..1000
FORMULA
Dirichlet g.f.: zeta(s-2)*zeta(s-3)/zeta(2*s-4).
Multiplicative with a(p^e) = p^e*p^(2*e-1)*(p+1). - Vladeta Jovovic, Nov 16 2001
a(n) = sum_{d|n} mu(d)*sigma(n^3/d^2). - Benoit Cloitre, Feb 16 2008
Sum_{k=1..n} a(k) ~ 15*n^4 / (4*Pi^2). - Vaclav Kotesovec, Feb 01 2019
Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + p/((p+1)*(p^3-1))) = 1.1392293101137663761606045655621290749920977339371831842000361508083066155... - Vaclav Kotesovec, Sep 20 2020
MATHEMATICA
a[n_] := n*DivisorSum[n, MoebiusMu[n/#] DivisorSigma[1, #^2]&]; Array[a, 40] (* Jean-François Alcover, Dec 02 2015 *)
PROG
(PARI) a(n)=direuler(p=2, n, (1+p^2*X)/(1-p^3*X))[n]
(PARI) a(n)=sumdiv(n, d, moebius(d)*sigma(n^3/d^2)) \\ Benoit Cloitre, Feb 16 2008
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
EXTENSIONS
Additional comments from Michael Somos, May 19 2000
STATUS
approved