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A087782 a(n) = number of solutions to x^3 + x == 0 (mod n). 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A084580 A263633 A171850 * A296774 A066099 A254111

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

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Last modified March 30 10:31 EDT 2020. Contains 333125 sequences. (Running on oeis4.)