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 A224516 #18 Sep 19 2020 10:30:57 %S A224516 1,2,2,2,2,4,4,2,4,4,2,4,4,8,4,2,2,8,4,4,8,4,2,4,2,8,4,8,2,8,4,2,4,4, %T A224516 8,8,4,8,8,4,2,16,4,4,8,4,2,4,4,4,4,8,2,8,4,8,8,4,2,8,4,8,16,2,8,8,4, %U A224516 4,4,16,2,8,4,8,4,8,8,16,4,4,4,4,2,16,4 %N A224516 Number of solutions to x^4 - x == 0 (mod n). %H A224516 Eric M. Schmidt, <a href="/A224516/b224516.txt">Table of n, a(n) for n = 1..10000</a> %F A224516 Multiplicative with a(p^e) = 4 for p == 1 (mod 3); a(p^e) = 2 for p == 2 (mod 3); a(3^1) = 2; a(3^e) = 4 for e > 1. %e A224516 The solutions for n = 7 are 0, 1, 2, and 4. %t A224516 f[3, e_] := If[e == 1, 2, 4]; f[p_, e_] := If[Mod[p, 3] == 2, 2, 4]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Sep 19 2020 *) %o A224516 (Sage) %o A224516 def A224516(n) : %o A224516 res = 1 %o A224516 for p, m in factor(n) : %o A224516 if (p % 3 == 2) or (p == 3 and m == 1) : res *= 2 %o A224516 else : res *= 4 %o A224516 return res %Y A224516 Cf. A034444, A087688, A060839, A000086. %K A224516 nonn,mult,easy %O A224516 1,2 %A A224516 _Eric M. Schmidt_, Apr 09 2013