A087122 a(n) is the number of non-congruent solutions to x^2*y^2 == 0 (mod n).

1, 3, 5, 12, 9, 15, 13, 32, 45, 27, 21, 60, 25, 39, 45, 128, 33, 135, 37, 108, 65, 63, 45, 160, 225, 75, 189, 156, 57, 135, 61, 320, 105, 99, 117, 540, 73, 111, 125, 288, 81, 195, 85, 252, 405, 135, 93, 640, 637, 675, 165, 300, 105, 567, 189, 416, 185, 171, 117, 540, 121, 183, 585, 1280, 225, 315, 133, 396, 225, 351

Offset: 1

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 18 2003

Keywords

• mult
• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A078430, A018804.

Programs

Mathematica

a[n_] := Product[{p, e} = pe; p^(e+Floor[e/2]-1)((p-1) Ceiling[e/2]+p), {pe, FactorInteger[n]}];
a /@ Range[1, 100] (* Jean-François Alcover, Sep 20 2019 *)

PARI

a(n)={my(f=factor(n)); prod(i=1, #f~, my(p=f[i,1], e=f[i,2]); p^(e + e\2 - 1)*((p-1)*((e+1)\2) + p))} \\ Andrew Howroyd, Jul 15 2018

Formula

Multiplicative with a(p^e) = p^(e + floor(e/2) - 1)*((p-1)*ceiling(e/2) + p). - Andrew Howroyd, Jul 15 2018