A363590 a(n) = Sum_{d|n, d odd} d^d.

1, 1, 28, 1, 3126, 28, 823544, 1, 387420517, 3126, 285311670612, 28, 302875106592254, 823544, 437893890380862528, 1, 827240261886336764178, 387420517, 1978419655660313589123980, 3126, 5842587018385982521381947992, 285311670612

Offset: 1

Author

Seiichi Manyama, Jul 08 2023

Keywords

• nonn
• easy

Comments

Not multiplicative: a(3)*a(5) != a(15), for example.

Crossrefs

Cf. A062796, A333823, A333824.

Cf. A000593, A050999, A051000, A292919, A363991.

Programs

Mathematica

a[n_] := DivisorSum[n, #^# &, OddQ[#] &]; Array[a, 20] (* Amiram Eldar, Jul 26 2023 *)

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

Formula

G.f.: Sum_{k>0} ((2*k-1) * x)^(2*k-1) / (1 - x^(2*k-1)).

a(2^n) = 1.