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A087694 Number of solutions to x^2 + xy + y^2 == 0 (mod n). 2
1, 1, 3, 4, 1, 3, 13, 4, 9, 1, 1, 12, 25, 13, 3, 16, 1, 9, 37, 4, 39, 1, 1, 12, 25, 25, 27, 52, 1, 3, 61, 16, 3, 1, 13, 36, 73, 37, 75, 4, 1, 39, 85, 4, 9, 1, 1, 48, 133, 25, 3, 100, 1, 27, 1, 52, 111, 1, 1, 12, 121, 61, 117, 64, 25, 3, 133, 4, 3, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

FORMULA

Multiplicative with a(3^e) = 3^e, a(p^e) = ((p-1)*e+p)*p^(e-1) if p mod 3 = 1, a(p^e) = p^(2*floor(e/2)) if p mod 3 = 2. - Vladeta Jovovic, Sep 27 2003

MAPLE

A087694 := proc(n) option remember; local pf, p, f, e ; if n = 1 then 1; else pf := ifactors(n)[2] ; if nops(pf) = 1 then f := op(1, pf) ; p := op(1, f) ; e := op(2, f) ; if p = 3 then n ; elif p mod 3 =1 then ((p-1)*e+p)*p^(e-1) ; else p^(2*floor(e/2)) ; end if; else mul(procname(op(1, p)^op(2, p)), p=pf) ; end if; end if; end proc:

seq(A087694(n), n=1..70) ; # R. J. Mathar, Jan 07 2011

MATHEMATICA

a[n_] := If[n==1, 1, Product[{p, e} = pe; Which[p==3, 3^e, Mod[p, 3] == 2, (p^2)^Quotient[e, 2], True, ((p-1) e + p) p^(e-1)], {pe, FactorInteger[n] }]];

a /@ Range[1, 100] (* Jean-Fran├žois Alcover, Sep 20 2019, from PARI *)

PROG

(PARI) a(n)={my(f=factor(n)); prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if(p==3, 3^e, if(p%3==2, (p^2)^(e\2), ((p-1)*e+p)*p^(e-1))))} \\ Andrew Howroyd, Jul 09 2018

CROSSREFS

Cf. A000086.

Sequence in context: A131228 A238558 A131129 * A010262 A201516 A105579

Adjacent sequences:  A087691 A087692 A087693 * A087695 A087696 A087697

KEYWORD

mult,nonn

AUTHOR

Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 27 2003

STATUS

approved

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Last modified August 8 19:29 EDT 2020. Contains 336298 sequences. (Running on oeis4.)