|
|
A087688
|
|
a(n) = number of solutions to x^3 - x == 0 (mod n).
|
|
3
|
|
|
1, 2, 3, 3, 3, 6, 3, 5, 3, 6, 3, 9, 3, 6, 9, 5, 3, 6, 3, 9, 9, 6, 3, 15, 3, 6, 3, 9, 3, 18, 3, 5, 9, 6, 9, 9, 3, 6, 9, 15, 3, 18, 3, 9, 9, 6, 3, 15, 3, 6, 9, 9, 3, 6, 9, 15, 9, 6, 3, 27, 3, 6, 9, 5, 9, 18, 3, 9, 9, 18
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Multiplicative with a(p^e) = 3 for p an odd prime, a(2^1) = 2, a(2^2) = 3, a(2^e) = 5 for e >= 3. - Eric M. Schmidt, Apr 08 2013
|
|
MAPLE
|
A087688 := proc(n) local a, x ; a := 0 ; for x from 0 to n-1 do if (x*(x^2-1)) mod n = 0 then a := a+1 ; end if; end do; a ; end proc:
|
|
MATHEMATICA
|
nsols[n_]:=Length[Select[Range[0, n-1], Mod[#^3-#, n]==0&]]; nsols/@Range[80] (* Harvey P. Dale, Mar 22 2011 *)
f[2, e_] := Which[e == 1, 2, e == 2, 3, e >= 3, 5]; f[p_, e_] := 3; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 19 2020 *)
|
|
PROG
|
(PARI) a(n)=if(n%2, 3^omega(n), my(v=valuation(n, 2)); 3^omega(n>>v)*[2, 3, 5][min(3, v)]) \\ Charles R Greathouse IV, Mar 22 2011
|
|
CROSSREFS
|
|
|
KEYWORD
|
mult,nonn,easy
|
|
AUTHOR
|
Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 27 2003
|
|
STATUS
|
approved
|
|
|
|