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A206590
Number of solutions (n,k) of k^3=n^3 (mod n), where 1<=k<n.
4
0, 0, 1, 0, 0, 0, 3, 2, 0, 0, 1, 0, 0, 0, 3, 0, 2, 0, 1, 0, 0, 0, 3, 4, 0, 8, 1, 0, 0, 0, 7, 0, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 1, 2, 0, 0, 3, 6, 4, 0, 1, 0, 8, 0, 3, 0, 0, 0, 1, 0, 0, 2, 15, 0, 0, 0, 1, 0, 0, 0, 11, 0, 0, 4, 1, 0, 0, 0, 3, 8, 0, 0, 1, 0, 0, 0, 3, 0, 2, 0, 1, 0, 0, 0, 7, 0, 6, 2
OFFSET
2,7
LINKS
EXAMPLE
8 divides exactly 3 of the numbers 8^3-k^3 for k = 1, 2 , ..., 7, so that a(8) = 3.
MATHEMATICA
f[n_, k_] := If[Mod[n^3 - k^3, n] == 0, 1, 0];
t[n_] := Flatten[Table[f[n, k], {k, 1, n - 1}]]
a[n_] := Count[Flatten[t[n]], 1]
Table[a[n], {n, 2, 120}] (* A206590 *)
PROG
(PARI) A206590(n) = { my(n3 = n^3); sum(k=1, n-1, !((n3-(k^3))%n)); }; \\ Antti Karttunen, Nov 17 2017
CROSSREFS
Cf. A206825.
Sequence in context: A324881 A350734 A305930 * A206825 A336551 A292380
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 09 2012
STATUS
approved