A242444 Number of squares k^2 < n with k^2*p == 1 (mod n) for some prime p < n.

0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 1, 0, 0, 2, 0, 2, 0, 0, 1, 1, 0, 2, 1, 2, 0, 2, 0, 3, 0, 1, 1, 1, 1, 2, 1, 0, 0, 2, 1, 2, 2, 1, 1, 2, 0, 3, 0, 1, 2, 2, 2, 1, 0, 2, 2, 2, 0, 1, 3, 0, 2, 2, 2, 2, 1, 2, 0, 2, 0, 2, 2, 2, 2, 3, 1, 3, 0

Offset

1,11

Comments

According to the conjecture in A242441, a(n) > 0 for all n > 1848.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

 a(9) = 1 since 2^2*7 == 1 (mod 9).

Mathematica

r[k_, n_]:=PowerMod[k^2, -1, n]
Do[m=0; Do[If[GCD[k, n]==1&&PrimeQ[r[k, n]], m=m+1], {k, 1, Sqrt[n-1]}]; Print[n, " ", m]; Continue, {n, 1, 80}]

Crossrefs

Cf. A000040, A000290, A242425, A242441.

Sequence in context: A302233 A214772 A332036 * A236441 A327695 A345446

Adjacent sequences: A242441 A242442 A242443 * A242445 A242446 A242447

Keyword

nonn

Author

Zhi-Wei Sun, May 14 2014

Status

approved