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
Crossrefs
Cf. A364041.
Programs
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Mathematica
a[n_] := DivisorSum[n, #^(# + 1) &, OddQ[#] &]; Array[a, 22] (* Amiram Eldar, Jul 09 2023 *)
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PARI
a(n) = sumdiv(n, d, (d%2==1)*d^(d+1));
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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
Formula
G.f.: Sum_{k>0} (2*k-1)^(2*k) * x^(2*k-1) / (1 - x^(2*k-1)).
a(2^n) = 1.