A323704 Number of cubic residues (including 0) modulo the n-th prime.

2, 3, 5, 3, 11, 5, 17, 7, 23, 29, 11, 13, 41, 15, 47, 53, 59, 21, 23, 71, 25, 27, 83, 89, 33, 101, 35, 107, 37, 113, 43, 131, 137, 47, 149, 51, 53, 55, 167, 173, 179, 61, 191, 65, 197, 67, 71, 75, 227, 77, 233, 239, 81, 251, 257, 263, 269, 91, 93, 281, 95, 293

Offset: 1

Author

Florian Severin, Jan 24 2019

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A046530, A000040, A236959.

Programs

Mathematica

Table[With[{p=Prime[n]},If[Mod[p,3]==1,1+(p-1)/3,p]],{n,80}] (* Harvey P. Dale, Feb 02 2025 *)

PARI

a(n) = my(p=prime(n)); sum(k=0, p-1, ispower(Mod(k,p), 3)); \\ Michel Marcus, Feb 26 2019

Python

from sympy import prime
def a(n):
  p = prime(n)
  return len(set([x**3 % p for x in range(p)]))

Formula

If prime(n) - 1 = 3k then a(n) = k+1, otherwise a(n) = prime(n). (Cf. formula for A236959.)

a(n) = A236959(n) + 1.

a(n) = A046530(A000040(n)). - Rémy Sigrist, Jan 24 2019