OFFSET
1,2
COMMENTS
Multiplicative because this sequence is the Dirichlet convolution of A000578 and A000593 which are both multiplicative. - Andrew Howroyd, Jul 27 2018
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
From Amiram Eldar, Nov 13 2022: (Start)
a(n) = A027847(n) for odd n.
Multiplicative with a(2^e) = (8^(e+1)-1)/7 and a(p^e) = (p^(3*e+5) - (p^2+p+1)*p^(e+1) + p + 1)/((p^3-1)*(p^2-1)) for p > 2.
Sum_{k=1..n} a(k) ~ c * n^4, where c = 7*Pi^4*zeta(3)/2880 = (7/32)*zeta(3)*zeta(4) = (7/32) * A183700 = 0.284596... . (End)
MATHEMATICA
f[p_, e_] := (p^(3*e+5) - (p^2+p+1)*p^(e+1) + p + 1)/((p^3-1)*(p^2-1)); f[2, e_] := (8^(e+1)-1)/7; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Nov 13 2022 *)
PROG
(PARI) a(n)={sumdiv(n, d, (n/d)^3*sigma(d>>valuation(d, 2)))} \\ Andrew Howroyd, Jul 27 2018
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Seiichi Manyama, Jun 09 2017
STATUS
approved