This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372998 #15 May 20 2024 02:29:32
%S A372998 1,16,81,270,625,1296,2401,4362,6639,10000,14641,21870,28561,38416,
%T A372998 50625,69890,83521,106224,130321,168750,194481,234256,279841,353322,
%U A372998 391245,456976,538071,648270,707281,810000,923521,1118450,1185921,1336336,1500625,1792530
%N A372998 a(n) = Sum_{k=1..n} sigma( (n/gcd(k,n))^3 ).
%H A372998 Amiram Eldar, <a href="/A372998/b372998.txt">Table of n, a(n) for n = 1..10000</a>
%F A372998 If k is squarefree (cf. A005117) then a(k) = k^4.
%F A372998 a(n) = Sum_{d|n} phi(d) * sigma(d^3).
%F A372998 From _Amiram Eldar_, May 20 2024: (Start)
%F A372998 Multiplicative with a(p^e) = (p^(4*e+4)-1)/(p^4-1) - (p^e-1)/(p-1).
%F A372998 Sum_{k=1..n} a(k) ~ c * n^5 / 5, where c = zeta(4) * zeta(5) * Product_{p prime} (1 - 1/p^4 - 1/p^5 + 1/p^6) = 1.01649108704844291655... . (End)
%t A372998 a[n_] := DivisorSum[n, EulerPhi[#] * DivisorSigma[1, #^3] &]; Array[a, 100] (* _Amiram Eldar_, May 20 2024 *)
%o A372998 (PARI) a(n) = sumdiv(n, d, eulerphi(d)*sigma(d^3));
%Y A372998 Cf. A005117.
%Y A372998 Cf. A013662, A013663.
%K A372998 nonn,mult
%O A372998 1,2
%A A372998 _Seiichi Manyama_, May 19 2024