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A333824
a(n) = Sum_{d|n, n/d odd} (n/d)^d.
3
1, 1, 4, 1, 6, 10, 8, 1, 37, 26, 12, 82, 14, 50, 384, 1, 18, 811, 20, 626, 2552, 122, 24, 6562, 3151, 170, 20440, 2402, 30, 74900, 32, 1, 178512, 290, 94968, 538003, 38, 362, 1596560, 390626, 42, 4901060, 44, 14642, 16364502, 530, 48, 43046722, 823593, 9766251
OFFSET
1,3
LINKS
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
Sequence in context: A210228 A209161 A338171 * A083843 A094264 A298829
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 06 2020
STATUS
approved