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A333823
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a(n) = Sum_{d|n, d odd} (n/d)^d.
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3
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1, 2, 4, 4, 6, 14, 8, 8, 37, 42, 12, 76, 14, 142, 384, 16, 18, 746, 20, 1044, 2552, 2070, 24, 536, 3151, 8218, 20440, 16412, 30, 41574, 32, 32, 178512, 131106, 94968, 263908, 38, 524326, 1596560, 32808, 42, 2379874, 44, 4194348, 16364502, 8388654, 48, 4144, 823593, 33654482
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} k * x^k / (1 - k^2*x^(2*k)).
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MATHEMATICA
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Table[DivisorSum[n, (n/#)^# &, OddQ[#] &], {n, 50}]
nmax = 50; CoefficientList[Series[Sum[k x^k/(1 - k^2 x^(2 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
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PROG
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(PARI) a(n) = sumdiv(n, d, if ((d)%2, (n/d)^d)); \\ Michel Marcus, Apr 07 2020
(Python)
from sympy import divisors
def A333823(n): return sum((n//d)**d for d in divisors(n>>(~n & n-1).bit_length(), generator=True)) # Chai Wah Wu, Jul 09 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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