A366418 - OEIS

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.

a(n) = n if there are more than n/2 distinct integers x^n mod n. - David A. Corneth, Oct 16 2023

LINKS

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

David A. Corneth, PARI program

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

(PARI) See PARI link \\ David A. Corneth, Oct 16 2023

CROSSREFS

Cf. A121278, A366419, A195637.

Sequence in context: A181805 A369450 A212010 * A328745 A357134 A003967

Adjacent sequences: A366415 A366416 A366417 * A366419 A366420 A366421

KEYWORD

nonn

AUTHOR

Albert Mukovskiy, Oct 11 2023

STATUS

approved