A087782 a(n) = number of solutions to x^3 + x == 0 (mod n).

1, 2, 1, 1, 3, 2, 1, 1, 1, 6, 1, 1, 3, 2, 3, 1, 3, 2, 1, 3, 1, 2, 1, 1, 3, 6, 1, 1, 3, 6, 1, 1, 1, 6, 3, 1, 3, 2, 3, 3, 3, 2, 1, 1, 3, 2, 1, 1, 1, 6, 3, 3, 3, 2, 3, 1, 1, 6, 1, 3, 3, 2, 1, 1, 9, 2, 1, 3, 1, 6, 1, 1, 3, 6, 3, 1, 1, 6, 1, 3, 1, 6, 1, 1, 9, 2, 3, 1, 3, 6, 3, 1, 1, 2, 3, 1, 3, 2, 1, 3, 3, 6, 1, 3, 3

Offset

1,2

Comments

Shadow transform of A034262. - Michel Marcus, Jun 06 2013

Links

Andrew Howroyd, 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(2^1) = 2, a(2^e) = 1 for e > 1, a(p^e) = 3 for p mod 4 == 1, a(p^e) = 1 for p mod 4 == 3. - Andrew Howroyd, Jul 15 2018

Mathematica

a[n_] := If[n == 1, 1, Product[{p, e} = pe; If[p == 2, If[e == 1, 2, 1], If[Mod[p, 4] == 1, 3, 1]], {pe, FactorInteger[n]}]];
a /@ Range[1, 100] (* Jean-François Alcover, Sep 20 2019 *)

Prog

(PARI) a(n)={my(v=vector(n)); sum(i=0, n-1, lift(Mod(i, n)^3 + i) == 0)} \\ 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, 2, 1), if(p%4==1, 3, 1)))} \\ Andrew Howroyd, Jul 15 2018

Crossrefs

Cf. A087688, A000089, A034262.

Sequence in context: A263633 A171850 A356144 * A337243 A296774 A066099

Adjacent sequences: A087779 A087780 A087781 * A087783 A087784 A087785

Keyword

mult,nonn

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 06 2003

Extensions

More terms from David Wasserman, Jun 17 2005

Status

approved