A366420 -id:A366420 - cp's OEIS frontend

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

Albert Mukovskiy, Oct 11 2023

nonn

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).

Cf. A366418, A121278, A366420, A365100.

a(n) = #setbinop((x, y)->Mod(x, n^3)^n+Mod(y, n^3)^n, [0..n^2-1]); \\ Michel Marcus, Oct 14 2023

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

cp's OEIS Frontend

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

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