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A087688 a(n) = number of solutions to x^3 - x == 0 (mod n). 3
1, 2, 3, 3, 3, 6, 3, 5, 3, 6, 3, 9, 3, 6, 9, 5, 3, 6, 3, 9, 9, 6, 3, 15, 3, 6, 3, 9, 3, 18, 3, 5, 9, 6, 9, 9, 3, 6, 9, 15, 3, 18, 3, 9, 9, 6, 3, 15, 3, 6, 9, 9, 3, 6, 9, 15, 9, 6, 3, 27, 3, 6, 9, 5, 9, 18, 3, 9, 9, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Shadow transform of A007531. - Michel Marcus, Jun 06 2013

a(n) = 3 iff n belongs to (A061345 \ {1}) Union {4}. - Bernard Schott, Sep 16 2019

LINKS

Eric M. Schmidt, Table of n, a(n) for n = 1..10000

Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150; see Definition 7 for the shadow transform.

N. J. A. Sloane, Transforms.

FORMULA

Multiplicative with a(p^e) = 3 for p an odd prime, a(2^1) = 2, a(2^2) = 3, a(2^e) = 5 for e >= 3. - Eric M. Schmidt, Apr 08 2013

MAPLE

A087688 := proc(n) local a, x ; a := 0 ; for x from 0 to n-1 do if (x*(x^2-1)) mod n = 0 then a := a+1 ; end if; end do; a ; end proc:

seq(A087688(n), n=1..70) ; # R. J. Mathar, Jan 07 2011

MATHEMATICA

nsols[n_]:=Length[Select[Range[0, n-1], Mod[#^3-#, n]==0&]]; nsols/@Range[80]  (* Harvey P. Dale, Mar 22 2011 *)

f[2, e_] := Which[e == 1, 2, e == 2, 3, e >= 3, 5]; f[p_, e_] := 3; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 19 2020 *)

PROG

(PARI) a(n)=if(n%2, 3^omega(n), my(v=valuation(n, 2)); 3^omega(n>>v)*[2, 3, 5][min(3, v)]) \\ Charles R Greathouse IV, Mar 22 2011

CROSSREFS

Cf. A034444, A224516, A060594.

Sequence in context: A134187 A078644 A133700 * A126854 A115206 A093653

Adjacent sequences:  A087685 A087686 A087687 * A087689 A087690 A087691

KEYWORD

mult,nonn,easy

AUTHOR

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

STATUS

approved

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Last modified May 13 17:46 EDT 2021. Contains 343864 sequences. (Running on oeis4.)