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Number of pairs 0 <= x <= y <= n-1 such that x^3 == y^3 (mod n).
5

%I #23 Oct 07 2024 09:07:36

%S 1,2,3,5,5,6,13,14,18,10,11,15,25,26,15,28,17,36,37,25,39,22,23,42,35,

%T 50,81,71,29,30,61,72,33,34,65,99,73,74,75,70,41,78,85,55,90,46,47,84,

%U 112,70,51,137,53,162,55,218,111,58,59,75,121,122,288,208,125,66,133,85,69,130,71,306,145,146,105,203,143,150,157

%N Number of pairs 0 <= x <= y <= n-1 such that x^3 == y^3 (mod n).

%C A087786 includes pairs (x,y) with x>y (which are excluded from the present sequence).

%H Seiichi Manyama, <a href="/A376757/b376757.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI) a(n) = sum(x=0, n-1, sum(y=x, n-1, Mod(x, n)^3 == Mod(y, n)^3)); \\ _Michel Marcus_, Oct 06 2024

%o (Python)

%o from collections import Counter

%o def A376757(n): return sum(d*(d+1)>>1 for d in Counter(pow(x,3,n) for x in range(n)).values()) # _Chai Wah Wu_, Oct 06 2024

%Y Cf. A000086, A087786, A046530, A290731, A376202, A376203, A376755, A376756.

%K nonn

%O 1,2

%A _Tom Duff_ and _N. J. A. Sloane_, Oct 06 2024