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A086932 Number of non-congruent solutions of x^2 + y^2 == -1 (mod n). 5
1, 2, 4, 0, 4, 8, 8, 0, 12, 8, 12, 0, 12, 16, 16, 0, 16, 24, 20, 0, 32, 24, 24, 0, 20, 24, 36, 0, 28, 32, 32, 0, 48, 32, 32, 0, 36, 40, 48, 0, 40, 64, 44, 0, 48, 48, 48, 0, 56, 40, 64, 0, 52, 72, 48, 0, 80, 56, 60, 0, 60, 64, 96, 0, 48, 96, 68, 0, 96, 64, 72, 0, 72, 72, 80, 0, 96, 96 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

L. Toth, Counting Solutions of Quadratic Congruences in Several Variables Revisited, J. Int. Seq. 17 (2014) # 14.11.6.

FORMULA

Multiplicative, with a(2^e) = 2 if e = 1 or 0 if e > 1, a(p^e) = (p-1)p^(e-1) if p == 1 (mod 4), a(p^e) = (p+1)p^(e-1) if p == 3 (mod 4). - Vladeta Jovovic, Sep 24 2003

MATHEMATICA

a[n_] := If[n == 1, 1, Module[{p, e}, Product[{p, e} = pe; Which[p == 2 && e == 1, 2, p == 2 && e > 1, 0, Mod[p, 4] == 1, (p - 1) p^(e - 1), Mod[p, 4] == 3, (p + 1) p^(e - 1)], {pe, FactorInteger[n]}]]];

a /@ Range[1, 100] (* Jean-Fran├žois Alcover, Sep 14 2019 *)

PROG

(PARI) a(n)={my(v=vector(n)); for(i=0, n-1, v[i^2%n + 1]++); sum(i=0, n-1, v[i+1]*v[(-1-i)%n + 1])} \\ Andrew Howroyd, Jul 15 2018

(PARI) a(n)={my(f=factor(n)); prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if(p==2, if(e>1, 0, 2), p^(e-1)*if(p%4==1, p-1, p+1)))} \\ Andrew Howroyd, Jul 15 2018

CROSSREFS

Cf. A060968.

Sequence in context: A327898 A140875 A115368 * A331762 A221255 A341862

Adjacent sequences:  A086929 A086930 A086931 * A086933 A086934 A086935

KEYWORD

mult,nonn

AUTHOR

Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 21 2003

EXTENSIONS

More terms from John W. Layman, Sep 25 2003

STATUS

approved

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Last modified July 30 09:18 EDT 2021. Contains 346359 sequences. (Running on oeis4.)