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 A372999 #14 May 22 2024 02:00:05
%S A372999 1,6,11,24,21,66,31,76,65,126,51,264,61,186,231,212,81,390,91,504,341,
%T A372999 306,111,836,201,366,299,744,141,1386,151,548,561,486,651,1560,181,
%U A372999 546,671,1596,201,2046,211,1224,1365,666,231,2332,409,1206,891,1464,261,1794
%N A372999 a(n) = Sum_{k=1..n} tau( (n/gcd(k,n))^4 ).
%H A372999 Amiram Eldar, <a href="/A372999/b372999.txt">Table of n, a(n) for n = 1..10000</a>
%F A372999 If p is prime, a(p) = 5*p - 4.
%F A372999 a(n) = Sum_{d|n} phi(d) * tau(d^4).
%F A372999 Multiplicative with a(p^e) = (4 - (4*e+5)*p^e + (4*e+1)*p^(e+1))/(p-1). - _Amiram Eldar_, May 21 2024
%t A372999 f[p_, e_] := (4 - (4*e+5)*p^e + (4*e+1)*p^(e+1))/(p-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, May 21 2024 *)
%o A372999 (PARI) a(n) = sumdiv(n, d, eulerphi(d)*numdiv(d^4));
%Y A372999 Cf. A062380, A062949, A372997.
%K A372999 nonn,mult
%O A372999 1,2
%A A372999 _Seiichi Manyama_, May 19 2024