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 A372997 #18 May 22 2024 01:59:55
%S A372997 1,5,9,19,17,45,25,59,51,85,41,171,49,125,153,163,65,255,73,323,225,
%T A372997 205,89,531,157,245,231,475,113,765,121,419,369,325,425,969,145,365,
%U A372997 441,1003,161,1125,169,779,867,445,185,1467,319,785,585,931,209,1155,697,1475
%N A372997 a(n) = Sum_{k=1..n} tau( (n/gcd(k,n))^3 ).
%H A372997 Amiram Eldar, <a href="/A372997/b372997.txt">Table of n, a(n) for n = 1..10000</a>
%F A372997 If p is prime, a(p) = 4*p - 3.
%F A372997 a(n) = Sum_{d|n} phi(d) * tau(d^3).
%F A372997 Multiplicative with a(p^e) = (3 - (3*e+4)*p^e + (3*e+1)*p^(e+1))/(p-1). - _Amiram Eldar_, May 21 2024
%t A372997 f[p_, e_] := (3 - (3*e+4)*p^e + (3*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 A372997 (PARI) a(n) = sumdiv(n, d, eulerphi(d)*numdiv(d^3));
%Y A372997 Cf. A062380, A062949, A372999.
%Y A372997 Cf. A000005, A000010, A344221.
%K A372997 nonn,mult
%O A372997 1,2
%A A372997 _Seiichi Manyama_, May 19 2024