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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,7

LINKS

Antti Karttunen, Table of n, a(n) for n = 2..16384

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: A292240 A324881 A305930 * A206825 A336551 A292380

Adjacent sequences:  A206587 A206588 A206589 * A206591 A206592 A206593

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 09 2012

STATUS

approved

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Last modified October 19 17:46 EDT 2021. Contains 348091 sequences. (Running on oeis4.)