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%I #30 Nov 14 2022 01:38:36
%S 1,16,81,272,625,1296,2401,4352,6642,10000,14641,22032,28561,38416,
%T 50625,69888,83521,106272,130321,170000,194481,234256,279841,352512,
%U 391250,456976,538002,653072,707281,810000,923521,1118208,1185921,1336336,1500625,1806624,1874161,2085136
%N a(n) = n^4 * Sum_{d^2|n} 1 / d^4.
%H Seiichi Manyama, <a href="/A351602/b351602.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = p^4*(p^(4*e) - p^(4*floor((e-1)/2)))/(p^4 - 1). - _Sebastian Karlsson_, Feb 25 2022
%F Sum_{k=1..n} a(k) ~ c * n^5, where c = zeta(6)/5 = Pi^6/4725 = 0.203468... . - _Amiram Eldar_, Nov 13 2022
%t f[p_, e_] := p^4*(p^(4*e) - p^(4*Floor[(e - 1)/2]))/(p^4 - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 40] (* _Amiram Eldar_, Nov 13 2022 *)
%o (PARI) a(n) = n^4*sumdiv(n, d, if (issquare(d), 1/d^2)); \\ _Michel Marcus_, Feb 15 2022
%Y Sequences of the form n^k * Sum_{d^2|n} 1/d^k for k = 0..10: A046951 (k=0), A340774 (k=1), A351600 (k=2), A351601 (k=3), this sequence (k=4), A351603 (k=5), A351604 (k=6), A351605 (k=7), A351606 (k=8), A351607 (k=9), A351608 (k=10).
%Y Cf. A013664.
%K nonn,mult
%O 1,2
%A _Wesley Ivan Hurt_, Feb 14 2022
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