The On-Line Encyclopedia of Integer Sequences (OEIS)

A366418 revision #13

A366418

Number of distinct integers of the form (x^n + y^n) mod n.

1, 2, 3, 3, 5, 6, 7, 3, 5, 10, 11, 9, 13, 14, 15, 3, 17, 6, 19, 9, 15, 22, 23, 9, 13, 26, 5, 21, 29, 30, 31, 3, 33, 34, 35, 9, 37, 38, 39, 9, 41, 18, 43, 33, 25, 46, 47, 9, 19, 10, 51, 30, 53, 6, 25, 21, 57, 58, 59, 27, 61, 62, 25, 3, 65, 66, 67, 39, 69, 70, 71, 9, 73, 74, 39

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OFFSET

1,2

COMMENTS

a(p) = p when p is prime. It appears that a(n) stabilizes for the subsequences n = k^m for each fixed k > 1 at large enough m.

LINKS

Table of n, a(n) for n=1..75.

PROG

(PARI) { a(n) = my(S, t); S=Set(); for(x=0, n-1, for(y=x, n-1, t=lift(Mod(x, n)^n+Mod(y, n)^n); S=setunion(S, [t]); ); ); #S }

(PARI) a(n) = #setbinop((x, y)->Mod(x, n)^n+Mod(y, n)^n, [0..n-1]); \\ Michel Marcus, Oct 12 2023

CROSSREFS

Cf. A121278, A366419, A195637.