%I #30 Feb 02 2025 12:01:14
%S 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,
%T 101,35,107,37,113,43,131,137,47,149,51,53,55,167,173,179,61,191,65,
%U 197,67,71,75,227,77,233,239,81,251,257,263,269,91,93,281,95,293
%N Number of cubic residues (including 0) modulo the n-th prime.
%H Harvey P. Dale, <a href="/A323704/b323704.txt">Table of n, a(n) for n = 1..1000</a>
%F If prime(n) - 1 = 3k then a(n) = k+1, otherwise a(n) = prime(n). (Cf. formula for A236959.)
%F a(n) = A236959(n) + 1.
%F a(n) = A046530(A000040(n)). - _Rémy Sigrist_, Jan 24 2019
%t Table[With[{p=Prime[n]},If[Mod[p,3]==1,1+(p-1)/3,p]],{n,80}] (* _Harvey P. Dale_, Feb 02 2025 *)
%o (Python)
%o from sympy import prime
%o def a(n):
%o p = prime(n)
%o return len(set([x**3 % p for x in range(p)]))
%o (PARI) a(n) = my(p=prime(n)); sum(k=0, p-1, ispower(Mod(k,p), 3)); \\ _Michel Marcus_, Feb 26 2019
%Y Cf. A046530, A000040, A236959.
%K nonn
%O 1,1
%A _Florian Severin_, Jan 24 2019