OFFSET
1,2
COMMENTS
Inverse Moebius transform applied twice to A001227.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: Sum_{k>=1} tau_3(k) * x^k / (1 - x^(2*k)), where tau_3 = A007425.
a(n) = tau_4(n) if n odd, tau_4(n) - tau_4(n/2) if n even, where tau_4 = A007426.
a(n) = Sum_{d|n, n/d odd} tau_3(d).
Product_{n>=1} 1 / (1 - x^n)^a(n) = g.f. for A280486.
Multiplicative with a(2^e) = (e+1)*(e+2)/2, and a(p^e) = (e+1)*(e+2)*(e+3)/6 for odd primes p. - Amiram Eldar, Dec 02 2020
MATHEMATICA
Table[Sum[DivisorSigma[0, n/d] Total[Mod[Divisors[d], 2]], {d, Divisors[n]}], {n, 1, 75}]
nmax = 75; A007425 = Table[DivisorSum[n, DivisorSigma[0, #] &], {n, 1, nmax}]; Table[DivisorSum[n, A007425[[#]] &, OddQ[n/#] &], {n, 1, nmax}]
f[2, e_] := (e + 1)*(e + 2)/2; f[p_, e_] := (e + 1)*(e + 2)*(e + 3)/6; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Dec 02 2020 *)
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Ilya Gutkovskiy, Oct 18 2019
STATUS
approved