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A308672 a(n) = Sum_{d|n} d^(d^3). 1

%I

%S 1,257,7625597484988,340282366920938463463374607431768211713,

%T 2350988701644575015937473074444491355637331113544175043017503412556834518909454345703126

%N a(n) = Sum_{d|n} d^(d^3).

%C The next term (a(6)) has 169 digits. - _Harvey P. Dale_, Sep 08 2020

%F L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(k^3-1))) = Sum_{k>=1} a(k)*x^k/k.

%t Table[Total[Divisors[n]^Divisors[n]^3],{n,5}] (* _Harvey P. Dale_, Sep 08 2020 *)

%t a[n_] := DivisorSum[n, #^(#^3) &]; Array[a, 5] (* _Amiram Eldar_, May 11 2021 *)

%o (PARI) {a(n) = sumdiv(n, d, d^d^3)}

%o (PARI) N=10; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^(k^(k^3-1))))))

%Y Column k=3 of A308674.

%Y Cf. A000005, A062796, A308671.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 16 2019

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Last modified October 18 06:43 EDT 2021. Contains 348065 sequences. (Running on oeis4.)