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a(n) = Sum_{d|n} max(d, n/d)^3.
4

%I #14 Jan 08 2018 02:58:44

%S 1,16,54,136,250,486,686,1152,1485,2250,2662,4016,4394,6174,7000,9280,

%T 9826,13554,13718,18250,19208,23958,24334,32560,31375,39546,40824,

%U 50078,48778,63182,59582,74752,74536,88434,86436,110106,101306,123462,123032,147024

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

%H Seiichi Manyama, <a href="/A297842/b297842.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) + A297793(n) = 2*A001158(n).

%t f[n_] := Block[{d = Divisors@ n}, Plus @@ (Max[#, n/#]^3 & /@ d)]; Array[f, 40] (* _Robert G. Wilson v_, Jan 07 2018 *)

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

%Y Sum_{d|n} max(d, n/d)^k: A117003 (k=1), A297841 (k=2), this sequence (k=3), A297843 (k=4), A297844 (k=5).

%Y Cf. A001158, A297793.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jan 07 2018