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A352038
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Sum of the 10th powers of the odd proper divisors of n.
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11
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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
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OFFSET
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1,6
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LINKS
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Table of n, a(n) for n=1..36.
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FORMULA
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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
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EXAMPLE
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a(10) = 9765626; a(10) = Sum_{d|10, d<10, d odd} d^10 = 1^10 + 5^10 = 9765626.
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Wesley Ivan Hurt, Mar 01 2022
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STATUS
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approved
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