cp's OEIS Frontend

A366420 Number of distinct integers of the form (x^n + y^n) mod n^4.

%I A366420 #23 Nov 16 2023 05:41:16
%S A366420 1,9,45,35,325,95,931,259,1215,625,6171,627,12337,2210,14625,2049,
%T A366420 32657,2435,58843,1683,11025,12105,140185,4883,40625,16055,32805,
%U A366420 14586,236321,11875,375751,16385,277695,59245,302575,16071,789913,97475,98865,13107,1413721,9405,1399693
%N A366420 Number of distinct integers of the form (x^n + y^n) mod n^4.
%C A366420 It is enough to take x,y from {0,1,...,n^3-1}.
%C A366420 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.
%C A366420 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).
%o A366420 (PARI) a(n) = #setbinop((x, y)->Mod(x, n^4)^n+Mod(y, n^4)^n, [0..n^3-1]); \\ _Michel Marcus_, Oct 14 2023
%o A366420 (Python)
%o A366420 def A366420(n):
%o A366420     m = n**4
%o A366420     return len({(pow(x,n,m)+pow(y,n,m))%m for x in range(n**3) for y in range(x+1)}) # _Chai Wah Wu_, Nov 12 2023
%Y A366420 Cf. A366418, A121278, A366419, A365101.
%K A366420 nonn
%O A366420 1,2
%A A366420 _Albert Mukovskiy_, Oct 11 2023