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A363590
a(n) = Sum_{d|n, d odd} d^d.
1
1, 1, 28, 1, 3126, 28, 823544, 1, 387420517, 3126, 285311670612, 28, 302875106592254, 823544, 437893890380862528, 1, 827240261886336764178, 387420517, 1978419655660313589123980, 3126, 5842587018385982521381947992, 285311670612
OFFSET
1,3
COMMENTS
Not multiplicative: a(3)*a(5) != a(15), for example.
FORMULA
G.f.: Sum_{k>0} ((2*k-1) * x)^(2*k-1) / (1 - x^(2*k-1)).
a(2^n) = 1.
MATHEMATICA
a[n_] := DivisorSum[n, #^# &, OddQ[#] &]; Array[a, 20] (* Amiram Eldar, Jul 26 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, (d%2==1)*d^d);
(Python)
from sympy import divisors
def A363590(n): return sum(d**d for d in divisors(n>>(~n & n-1).bit_length(), generator=True)) # Chai Wah Wu, Jul 09 2023
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jul 08 2023
STATUS
approved