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a(n) = Sum_{d|n} d^(3*d + 1).
7

%I #22 Jun 18 2019 14:51:00

%S 1,129,59050,67108993,152587890626,609359740069674,

%T 3909821048582988050,37778931862957228818561,

%U 523347633027360537213570571,10000000000000000000152587890754,255476698618765889551019445759400442,8505622499821102144576132293474637113130

%N a(n) = Sum_{d|n} d^(3*d + 1).

%H Seiichi Manyama, <a href="/A283535/b283535.txt">Table of n, a(n) for n = 1..152</a>

%F L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(3*k))) = Sum_{k>=1} a(k)*x^k/k. - _Seiichi Manyama_, Jun 18 2019

%e a(6) = 1^(3+1) + 2^(6+1) + 3^(9+1) + 6^(18+1) = 609359740069674.

%t f[n_] := Block[{d = Divisors[n]}, Total[d^(3 d + 1)]]; Array[f, 12] (* _Robert G. Wilson v_, Mar 10 2017 *)

%o (PARI) a(n) = sumdiv(n, d, d^(3*d+1)); \\ _Michel Marcus_, Mar 11 2017

%o (PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(3*k))))) \\ _Seiichi Manyama_, Jun 18 2019

%Y Cf. Sum_{d|n} d^(k*d+1): A283498 (k=1), A283533 (k=2), this sequence (k=3).

%Y Cf. A308697.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Mar 10 2017