OFFSET
1,6
LINKS
FORMULA
G.f.: Sum_{k>=1} (2*k-1) * x^(4*k-2) / (1 - x^(2*k-1)). - Ilya Gutkovskiy, Apr 13 2021
Sum_{k=1..n} a(k) ~ c * n^2, where c = (zeta(2)-1)/4 = 0.1612335167... . - Amiram Eldar, Oct 11 2023
EXAMPLE
The sum of odd divisors of 9 that are less than 9 is 1 + 3 = 4.
MATHEMATICA
f[2, e_] := 1; f[p_, e_] := (p^(e+1)-1)/(p-1); a[1] = 0; a[n_] := Times @@ f @@@ FactorInteger[n] - If[OddQ[n], n, 0]; Array[a, 75] (* Amiram Eldar, Oct 11 2023 *)
PROG
(PARI) a(n) = sumdiv(n , d, (d%2) * (d<n) * d); \\ Michel Marcus, Jan 14 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Mohammad K. Azarian, Mar 04 2004
STATUS
approved