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

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, 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, 4, 4, 16, 2, 8, 4, 8, 4, 8, 8, 16, 4, 4, 4, 4, 2, 16, 4

Offset

1,2

Links

Eric M. Schmidt, Table of n, a(n) for n = 1..10000

Formula

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.

Example

The solutions for n = 7 are 0, 1, 2, and 4.

Mathematica

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 *)

Prog

(Sage)
def A224516(n) :
    res = 1
    for p, m in factor(n) :
        if (p % 3 == 2) or (p == 3 and m == 1) : res *= 2
        else : res *= 4
    return res

Crossrefs

Cf. A034444, A087688, A060839, A000086.

Sequence in context: A179004 A143979 A034877 * A023161 A023155 A277847

Adjacent sequences: A224513 A224514 A224515 * A224517 A224518 A224519

Keyword

nonn,mult,easy

Author

Eric M. Schmidt, Apr 09 2013

Status

approved