A337910 - OEIS

A337910

Integers of the form (the number of nonnegative bases m < n such that m^3 == m (mod n))/(the number of nonnegative bases m < n such that -m^3 == m (mod n)).

1, 1, 3, 3, 1, 3, 3, 5, 3, 1, 3, 9, 1, 3, 3, 5, 1, 3, 3, 3, 9, 3, 3, 15, 1, 1, 3, 9, 1, 3, 3, 5, 9, 1, 3, 9, 1, 3, 3, 5, 1, 9, 3, 9, 3, 3, 3, 15, 3, 1, 3, 3, 1, 3, 3, 15, 9, 1, 3, 9, 1, 3, 9, 5, 1, 9, 3, 3, 9, 3, 3, 15, 1, 1, 3, 9, 9, 3, 3, 5, 3, 1, 3, 27, 1, 3, 3, 15, 1, 3, 3, 9, 9, 3, 3, 15

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OFFSET

1,3

COMMENTS

All the terms are odd numbers.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

1 <= a(n) < n, for n > 3.

MAPLE

f:= proc(n) local x; nops([msolve(x^3=x, n)])/nops([msolve(-x^3=x, n)]) end proc:

f(1):= 1: f(2):= 1: f(3):= 3: f(6):= 3:

map(f, [$1..100]); # Robert Israel, Oct 30 2025

MATHEMATICA

a[n_] := Length[Solve[x^3 == x, x, Modulus -> n]] / Length[Solve[-x^3 == x, x, Modulus -> n]]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Apr 22 2026 *)

PROG

(Magma) [#[m: m in [0..n-1] | m^3 mod n eq m]/#[m: m in [0..n-1] | -m^3 mod n eq m]: n in [1..96]];

CROSSREFS

Cf. A026741, A008784, A002313, A002145, A334006.

Sequence in context: A083953 A066400 A125562 * A092040 A293866 A161200

Adjacent sequences: A337907 A337908 A337909 * A337911 A337912 A337913

KEYWORD

nonn,easy,mult

AUTHOR

Juri-Stepan Gerasimov, Sep 29 2020

STATUS

approved