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

1,2

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A078430, A018804.

Sequence in context: A343738 A066541 A279728 * A358336 A286900 A361111

Adjacent sequences: A087119 A087120 A087121 * A087123 A087124 A087125

Keyword

mult,nonn

Author

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

Status

approved