A062803 Number of solutions to x^2 == y^2 (mod n).

1, 2, 5, 8, 9, 10, 13, 24, 21, 18, 21, 40, 25, 26, 45, 64, 33, 42, 37, 72, 65, 42, 45, 120, 65, 50, 81, 104, 57, 90, 61, 160, 105, 66, 117, 168, 73, 74, 125, 216, 81, 130, 85, 168, 189, 90, 93, 320, 133, 130, 165, 200, 105, 162, 189, 312, 185, 114, 117, 360, 121, 122, 273

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

László Tóth, Counting Solutions of Quadratic Congruences in Several Variables Revisited, J. Int. Seq. 17 (2014) # 14.11.6.

Formula

a(n) is multiplicative and, for an odd prime p, a(p) = 2*p - 1.

Multiplicative with a(2^e)=e*2^e and a(p^e)=((p-1)*e+p)*p^(e-1) for an odd prime p. - Vladeta Jovovic, Sep 22 2003

Mathematica

f[2, e_] := e*2^e; f[p_, e_] := ((p-1)*e+p)*p^(e-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 10 2020 *)

Crossrefs

Cf. A086933.

Sequence in context: A047620 A283205 A322916 * A231756 A212591 A153275

Adjacent sequences: A062800 A062801 A062802 * A062804 A062805 A062806

Keyword

nonn,mult,easy

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 19 2001

Extensions

More terms from Vladeta Jovovic, Sep 22 2003

Status

approved