A087122 - OEIS

%I #13 Sep 20 2019 07:54:25

%S 1,3,5,12,9,15,13,32,45,27,21,60,25,39,45,128,33,135,37,108,65,63,45,

%T 160,225,75,189,156,57,135,61,320,105,99,117,540,73,111,125,288,81,

%U 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

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

%H Andrew Howroyd, <a href="/A087122/b087122.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = p^(e + floor(e/2) - 1)*((p-1)*ceiling(e/2) + p). - _Andrew Howroyd_, Jul 15 2018

%t a[n_] := Product[{p, e} = pe; p^(e+Floor[e/2]-1)((p-1) Ceiling[e/2]+p), {pe, FactorInteger[n]}];

%t a /@ Range[1, 100] (* _Jean-François Alcover_, Sep 20 2019 *)

%o (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

%Y Cf. A078430, A018804.

%K mult,nonn

%O 1,2

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