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

%I #17 Jan 13 2025 01:32:29

%S 1,32,162,528,1250,2754,4802,8704,13203,21250,29282,44576,57122,81634,

%T 102500,139520,167042,225666,260642,341250,393764,497794,559682,

%U 715808,781875,971074,1076004,1310946,1414562,1743842,1847042,2236416,2401124,2839714,3006052

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

%H Seiichi Manyama, <a href="/A297843/b297843.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) + A297794(n) = 2*A001159(n).

%F Sum_{k=1..n} a(k) ~ (2*zeta(5)/5) * n^5. - _Amiram Eldar_, Jan 12 2025

%t f[n_] := Block[{d = Divisors@ n}, Plus @@ (Max[#, n/#]^4 & /@ d)]; Array[f, 35] (* _Robert G. Wilson v_, Jan 07 2018 *)

%o (PARI) {a(n) = sumdiv(n, d, max(d, n/d)^4)}

%Y Sum_{d|n} max(d, n/d)^k: A117003 (k=1), A297841 (k=2), A297842 (k=3), this sequence (k=4), A297844 (k=5).

%Y Cf. A001159, A013663, A297794.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jan 07 2018