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A208895 Number of non-congruent solutions to x^2 + y^2 + z^2 + t^2 == 1 (mod n). 10
1, 8, 24, 64, 120, 192, 336, 512, 648, 960, 1320, 1536, 2184, 2688, 2880, 4096, 4896, 5184, 6840, 7680, 8064, 10560, 12144, 12288, 15000, 17472, 17496, 21504, 24360, 23040, 29760, 32768, 31680, 39168, 40320, 41472, 50616, 54720, 52416, 61440, 68880, 64512 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..42.

L. Tóth, Counting solutions of quadratic congruences in several variables revisited, arXiv preprint arXiv:1404.4214 [math.NT], 2014.

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

FORMULA

Conjecture: a(n) = n*Sum_{d|2*n} d^2*mu(2*n/d)/3. - Gionata Neri, Feb 18 2018

MAPLE

A208895 := proc(n)

    local a, pe, p, nu ;

    a := 1 ;

    for pe in ifactors(n)[2] do

        p := op(1, pe) ;

        nu := op(2, pe) ;

        if p > 2 then

            a := a*p^(3*nu)*(1-1/p^2) ;

        else

            a := a*8^nu ;

        end if;

    end do:

    a ;

end proc:

seq(A208895(n), n=1..20) ; # R. J. Mathar, Jun 23 2018

MATHEMATICA

a[n_] := Length[Union[Flatten[Table[If[Mod[x^2 + y^2 + z^2 + t^2, n] == 1, {x, y, z, t}], {x, n}, {y, n}, {z, n}, {t, n}], 3]]] - 1; Join[{1}, Table[a[n], {n, 2, 30}]]

CROSSREFS

Cf. A060968, A087784.

Sequence in context: A066605 A066497 A205963 * A111071 A090336 A200253

Adjacent sequences:  A208892 A208893 A208894 * A208896 A208897 A208898

KEYWORD

nonn,mult

AUTHOR

José María Grau Ribas, Mar 03 2012

STATUS

approved

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Last modified June 19 00:37 EDT 2021. Contains 345125 sequences. (Running on oeis4.)