cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A363590 a(n) = Sum_{d|n, d odd} d^d.

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%I A363590 #38 Jul 26 2023 03:21:51
%S A363590 1,1,28,1,3126,28,823544,1,387420517,3126,285311670612,28,
%T A363590 302875106592254,823544,437893890380862528,1,827240261886336764178,
%U A363590 387420517,1978419655660313589123980,3126,5842587018385982521381947992,285311670612
%N A363590 a(n) = Sum_{d|n, d odd} d^d.
%C A363590 Not multiplicative: a(3)*a(5) != a(15), for example.
%F A363590 G.f.: Sum_{k>0} ((2*k-1) * x)^(2*k-1) / (1 - x^(2*k-1)).
%F A363590 a(2^n) = 1.
%t A363590 a[n_] := DivisorSum[n, #^# &, OddQ[#] &]; Array[a, 20] (* _Amiram Eldar_, Jul 26 2023 *)
%o A363590 (PARI) a(n) = sumdiv(n, d, (d%2==1)*d^d);
%o A363590 (Python)
%o A363590 from sympy import divisors
%o A363590 def A363590(n): return sum(d**d for d in divisors(n>>(~n & n-1).bit_length(),generator=True)) # _Chai Wah Wu_, Jul 09 2023
%Y A363590 Cf. A062796, A333823, A333824.
%Y A363590 Cf. A000593, A050999, A051000, A292919, A363991.
%K A363590 nonn,easy
%O A363590 1,3
%A A363590 _Seiichi Manyama_, Jul 08 2023