A363991 a(n) = Sum_{d|n, d odd} d^(d+1).

1, 1, 82, 1, 15626, 82, 5764802, 1, 3486784483, 15626, 3138428376722, 82, 3937376385699290, 5764802, 6568408355712906332, 1, 14063084452067724991010, 3486784483, 37589973457545958193355602, 15626, 122694327386105632949009377724, 3138428376722

Offset

1,3

Links

Table of n, a(n) for n=1..22.

Formula

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

a(2^n) = 1.

Mathematica

a[n_] := DivisorSum[n, #^(# + 1) &, OddQ[#] &]; Array[a, 22] (* Amiram Eldar, Jul 09 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (d%2==1)*d^(d+1));
(Python)
from sympy import divisors
def A363991(n): return sum(d**(d+1) for d in divisors(n>>(~n & n-1).bit_length(), generator=True)) # Chai Wah Wu, Jul 09 2023

Crossrefs

Cf. A364041.

Sequence in context: A347175 A352032 A051001 * A050678 A354501 A033402

Adjacent sequences: A363988 A363989 A363990 * A363992 A363993 A363994

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 09 2023

Status

approved