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A235872 Number of solutions to the equation x^2=0 in the ring of Gaussian integers modulo n. 1
1, 2, 1, 4, 1, 2, 1, 8, 9, 2, 1, 4, 1, 2, 1, 16, 1, 18, 1, 4, 1, 2, 1, 8, 25, 2, 9, 4, 1, 2, 1, 32, 1, 2, 1, 36, 1, 2, 1, 8, 1, 2, 1, 4, 9, 2, 1, 16, 49, 50, 1, 4, 1, 18, 1, 8, 1, 2, 1, 4, 1, 2, 9, 64, 1, 2, 1, 4, 1, 2, 1, 72, 1, 2, 25, 4, 1, 2, 1, 16, 81, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers of solutions to x^2 == y^2 (mod n), 2*x*y == 0 (mod n). - Andrew Howroyd, Aug 06 2018

LINKS

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

FORMULA

Multiplicative with a(2^e) = 2^e, a(p^e) = p^(2*floor(e/2)). - Andrew Howroyd, Aug 06 2018

MATHEMATICA

invoG[n_] := invoG[n] = Sum[If[Mod[(x + I y)^2, n] == 0, 1, 0], {x, 0, n - 1}, {y, 0, n - 1}]; Table[invoG[n], {n, 1, 104}]

PROG

(PARI) a(n)={sum(i=0, n-1, sum(j=0, n-1, (i^2 - j^2)%n == 0 && 2*i*j%n == 0))} \\ Andrew Howroyd, Aug 06 2018

(PARI) a(n)={my(f=factor(n)); prod(i=1, #f~, my([p, e]=f[i, ]); p^if(p==2, e, e - e%2))} \\ Andrew Howroyd, Aug 06 2018

CROSSREFS

Cf. A062803.

Sequence in context: A079891 A108738 A064405 * A100762 A059147 A091891

Adjacent sequences:  A235869 A235870 A235871 * A235873 A235874 A235875

KEYWORD

nonn,mult

AUTHOR

José María Grau Ribas, Apr 03 2014

STATUS

approved

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Last modified June 13 09:54 EDT 2021. Contains 344981 sequences. (Running on oeis4.)