OFFSET
1,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..5000
FORMULA
G.f.: Sum_{k>=1} (2*k - 1) * x^(2*k - 1) / (1 - (2*k - 1)*x^(2*k - 1)).
a(2^n) = 1. - Seiichi Manyama, Apr 07 2020
a(n) = Sum_{d|n, d odd} d^(n/d). - Chai Wah Wu, Jul 09 2023
MATHEMATICA
Table[DivisorSum[n, (n/#)^# &, OddQ[n/#] &], {n, 50}]
nmax = 50; CoefficientList[Series[Sum[(2 k - 1) x^(2 k - 1)/(1 - (2 k - 1) x^(2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(PARI) a(n) = sumdiv(n, d, if ((n/d)%2, (n/d)^d)); \\ Michel Marcus, Apr 07 2020
(Python)
from sympy import divisors
def A333824(n): return sum(d**(n//d) for d in divisors(n>>(~n & n-1).bit_length(), generator=True)) # Chai Wah Wu, Jul 09 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 06 2020
STATUS
approved