OFFSET
1,2
COMMENTS
Dirichlet convolution of A000593 with itself.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Sum_{k=1..n} a(k) ~ Pi^2 * n^2 * (Pi^2 * (log(n)/2 + log(2) + gamma - 1/4) + 6*zeta'(2)) / 144, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Oct 17 2019
Multiplicative with a(2^e) = e+1, and a(p^e) = ((e+1)*p^(e+3) - (e+3)*(p^(e+2) - p + 1) + 2)/(p-1)^3 for an odd prime p. - Amiram Eldar, Sep 15 2023
MATHEMATICA
nmax = 65; A000593 = Table[DivisorSum[n, Mod[#, 2] # &], {n, 1, nmax}]; Table[DivisorSum[n, A000593[[#]] A000593[[n/#]] &], {n, 1, nmax}]
f[p_, e_] := ((e+1)*p^(e+3) - (e+3)*(p^(e+2) - p + 1) + 2)/(p-1)^3; f[2, e_] := e+1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 15 2023 *)
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Ilya Gutkovskiy, Oct 16 2019
STATUS
approved