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A352038 Sum of the 10th powers of the odd proper divisors of n. 11
0, 1, 1, 1, 1, 59050, 1, 1, 59050, 9765626, 1, 59050, 1, 282475250, 9824675, 1, 1, 3486843451, 1, 9765626, 282534299, 25937424602, 1, 59050, 9765626, 137858491850, 3486843451, 282475250, 1, 576660215300, 1, 1, 25937483651, 2015993900450, 292240875, 3486843451 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..36.

FORMULA

a(n) = Sum_{d|n, d<n, d odd} d^10.

G.f.: Sum_{k>=1} (2*k-1)^10 * x^(4*k-2) / (1 - x^(2*k-1)). - Ilya Gutkovskiy, Mar 02 2022

EXAMPLE

a(10) = 9765626; a(10) = Sum_{d|10, d<10, d odd} d^10 = 1^10 + 5^10 = 9765626.

PROG

(Python)

from math import prod

from sympy import factorint

def A352038(n): return prod((p**(10*(e+1))-1)//(p**10-1) for p, e in factorint(n).items() if p > 2) - (n**10 if n % 2 else 0) # Chai Wah Wu, Mar 01 2022

CROSSREFS

Sum of the k-th powers of the odd proper divisors of n for k=0..10: A091954 (k=0), A091570 (k=1), A351647 (k=2), A352031 (k=3), A352032 (k=4), A352033 (k=5), A352034 (k=6), A352035 (k=7), A352036 (k=8), A352037 (k=9), this sequence (k=10).

Sequence in context: A017314 A017434 A017566 * A321814 A288886 A210172

Adjacent sequences:  A352035 A352036 A352037 * A352039 A352040 A352041

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Mar 01 2022

STATUS

approved

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Last modified July 1 15:17 EDT 2022. Contains 354973 sequences. (Running on oeis4.)