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 A359052 a(n) = Sum_{d|n} sigma_d(d)^n. 3

%I #18 Aug 27 2023 17:02:56

%S 1,26,21953,5554572467,298500366308609377,

%T 11413459460309090641106905930,

%U 256925761343390078522337875137209684721665,6476754651706496208416137876625690606583079440495100502628

%N a(n) = Sum_{d|n} sigma_d(d)^n.

%H Seiichi Manyama, <a href="/A359052/b359052.txt">Table of n, a(n) for n = 1..26</a>

%F G.f.: Sum_{k >= 1} (sigma_k(k) * x)^k/(1 - (sigma_k(k) * x)^k).

%t a[n_] := DivisorSum[n, DivisorSigma[#, #]^n &]; Array[a, 8] (* _Amiram Eldar_, Aug 27 2023 *)

%o (PARI) a(n) = sumdiv(n, d, sigma(d, d)^n);

%o (PARI) my(N=10, x='x+O('x^N)); Vec(sum(k=1, N, (sigma(k, k)*x)^k/(1-(sigma(k, k)*x)^k)))

%Y Cf. A344060, A359053, A359054.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Dec 14 2022

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Last modified September 16 19:55 EDT 2024. Contains 375977 sequences. (Running on oeis4.)