A305211 a(n) is the number of possible values of (x^3 + y^3) mod n, where x and y are any integers.

1, 2, 3, 4, 5, 6, 5, 8, 5, 10, 11, 12, 13, 10, 15, 16, 17, 10, 19, 20, 15, 22, 23, 24, 25, 26, 15, 20, 29, 30, 31, 32, 33, 34, 25, 20, 37, 38, 39, 40, 41, 30, 43, 44, 25, 46, 47, 48, 35, 50, 51, 52, 53, 30, 55, 40, 57, 58, 59, 60, 61, 62, 25, 64, 65, 66, 67

Offset: 1

Author

Jack Zhang, May 27 2018

Keywords

• nonn

Comments

Conjecture: keyword mult applies. Furthermore a procedure to find a(n) is as follows: if n = 7k then n -> 5*n/7. if n = 9k then n-> 5*n/9. return(n). - David A. Corneth, May 22 2020

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A155918 (with squares instead of cubes).

Programs

PARI

a(n) = my(v=[]); for (x=1, n, for (y=1, n, v = concat(v, Mod(x, n)^3 + Mod(y, n)^3))); #Set(v); \\ Michel Marcus, Jul 10 2018

PARI

a(n) = {my(v = Set(vector(n, i, i^3%n)), l); if(#v == n, return(n) , res = vector(n); for(i = 1, #v, for(j = i, #v, res[1 + (v[i] + v[j]) % n] = 1 ) ); vecsum(res) ) } \\ David A. Corneth, May 22 2020

Python

[len(set((pow(x,3,n)+pow(y,3,n))%n for x in range(n) for y in range(x+1))) for n in range(1,51)]

Extensions

a(50)-a(67) from Jon E. Schoenfield, May 28 2018