cp's OEIS Frontend

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.

A224516 Number of solutions to x^4 - x == 0 (mod n).

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%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