A366419 Number of distinct integers of the form (x^n + y^n) mod n^3.

1, 5, 15, 11, 65, 21, 133, 34, 135, 75, 561, 63, 949, 192, 975, 129, 1921, 165, 3097, 99, 525, 663, 6095, 231, 1625, 741, 1215, 576, 8149, 525, 12121, 513, 8415, 2091, 8645, 495, 21349, 3081, 2535, 363, 34481, 315, 32551, 1989, 8775, 5316, 51935, 903, 6517, 1875, 28815, 1062

Offset

1,2

Comments

It is enough to take x,y from {0,1,...,n^2-1}.

It appears that the number of distinct integers of the form x^(p^k) + y^(p^k) mod (p^k)^m for a prime p>2 and natural k is A121278(p)*p^(k-1)*p^(k*(m-2)) for m>1. For m=1 see A366418.

It appears that the number of distinct integers of the form x^n + y^n mod n^m for an odd n, m>1 is A121278(n)*n^(m-2).

Links

Table of n, a(n) for n=1..52.

Prog

(PARI) a(n) = #setbinop((x, y)->Mod(x, n^3)^n+Mod(y, n^3)^n, [0..n^2-1]); \\ Michel Marcus, Oct 14 2023
(Python)
def A366419(n):
    m = n**3
    return len({(pow(x, n, m)+pow(y, n, m))%m for x in range(n**2) for y in range(x+1)}) # Chai Wah Wu, Nov 13 2023

Crossrefs

Cf. A366418, A121278, A366420, A365100.

Sequence in context: A302841 A113259 A298265 * A309620 A291794 A321775

Adjacent sequences: A366416 A366417 A366418 * A366420 A366421 A366422

Keyword

nonn

Author

Albert Mukovskiy, Oct 11 2023

Status

approved