A363991 -id:A363991 - cp's OEIS frontend

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

Seiichi Manyama, Jul 08 2023

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

Cf. A062796, A333823, A333824.

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

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

PARI
```
a(n) = sumdiv(n, d, (d%2==1)*d^d);
```

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

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

a(2^n) = 1.

A364041 Expansion of 1/Product_{k>0} (1 - x^(2k-1))^((2k-1)^(2*k-1)).

Original entry on oeis.org

1, 1, 1, 28, 28, 3153, 3531, 827074, 911449, 388335592, 415455628, 285728307489, 298762259972, 303174312029604, 312427539531172, 438206538943092800, 447594828079035405, 827688010429432132457, 840767646450714838158, 1979260573433349667269165

Offset: 0

Seiichi Manyama, Jul 09 2023

nonn

Cf. A023880, A363991.

a[0] = 1; a[n_] := a[n] = Sum[DivisorSum[k, #^(# + 1) &, OddQ[#] &]*a[n - k], {k, 1, n}]/n; Array[a, 20, 0] (* Amiram Eldar, Jul 09 2023 *)

my(N=20, x='x+O('x^N)); Vec(1/prod(k=1, N, (1-x^(2*k-1))^((2*k-1)^(2*k-1))))

G.f.: exp( Sum_{k>0} A363991(k) * x^k/k ).

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} A363991(k) * a(n-k).

cp's OEIS Frontend

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

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A364041 Expansion of 1/Product_{k>0} (1 - x^(2k-1))^((2k-1)^(2*k-1)).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

Formula

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

PARI

Python

Formula

A364041 Expansion of 1/Product_{k>0} (1 - x^(2*k-1))^((2*k-1)^(2*k-1)).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

Formula

A364041 Expansion of 1/Product_{k>0} (1 - x^(2k-1))^((2k-1)^(2*k-1)).