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A087122 a(n) is the number of non-congruent solutions to x^2*y^2 == 0 (mod n). 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A320433 A066541 A279728 * A286900 A037221 A182537

Adjacent sequences:  A087119 A087120 A087121 * A087123 A087124 A087125

KEYWORD

mult,nonn

AUTHOR

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

STATUS

approved

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Last modified April 5 16:37 EDT 2020. Contains 333245 sequences. (Running on oeis4.)