login
A224516
Number of solutions to x^4 - x == 0 (mod n).
2
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
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
KEYWORD
nonn,mult,easy
AUTHOR
Eric M. Schmidt, Apr 09 2013
STATUS
approved