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

%I A363991 #38 Jul 09 2023 12:13:38
%S A363991 1,1,82,1,15626,82,5764802,1,3486784483,15626,3138428376722,82,
%T A363991 3937376385699290,5764802,6568408355712906332,1,
%U A363991 14063084452067724991010,3486784483,37589973457545958193355602,15626,122694327386105632949009377724,3138428376722
%N A363991 a(n) = Sum_{d|n, d odd} d^(d+1).
%F A363991 G.f.: Sum_{k>0} (2*k-1)^(2*k) * x^(2*k-1) / (1 - x^(2*k-1)).
%F A363991 a(2^n) = 1.
%t A363991 a[n_] := DivisorSum[n, #^(# + 1) &, OddQ[#] &]; Array[a, 22] (* _Amiram Eldar_, Jul 09 2023 *)
%o A363991 (PARI) a(n) = sumdiv(n, d, (d%2==1)*d^(d+1));
%o A363991 (Python)
%o A363991 from sympy import divisors
%o A363991 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
%Y A363991 Cf. A364041.
%K A363991 nonn,easy
%O A363991 1,3
%A A363991 _Seiichi Manyama_, Jul 09 2023