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

%I A305211 #30 Jun 15 2020 21:17:49
%S A305211 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,
%T A305211 15,20,29,30,31,32,33,34,25,20,37,38,39,40,41,30,43,44,25,46,47,48,35,
%U A305211 50,51,52,53,30,55,40,57,58,59,60,61,62,25,64,65,66,67
%N A305211 a(n) is the number of possible values of (x^3 + y^3) mod n, where x and y are any integers.
%C A305211 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
%H A305211 David A. Corneth, <a href="/A305211/b305211.txt">Table of n, a(n) for n = 1..10000</a>
%o A305211 (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)]
%o A305211 (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
%o A305211 (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
%Y A305211 Cf. A155918 (with squares instead of cubes).
%K A305211 nonn
%O A305211 1,2
%A A305211 _Jack Zhang_, May 27 2018
%E A305211 a(50)-a(67) from _Jon E. Schoenfield_, May 28 2018