A206714 - OEIS

A206714

Number of solutions (n,k) of s(k)=s(n) (mod n), where 1<=k<n and s(k)=2^(k-1).

0, 1, 1, 1, 2, 2, 4, 1, 2, 1, 4, 1, 4, 3, 11, 2, 2, 1, 4, 3, 2, 2, 10, 1, 2, 1, 8, 1, 7, 6, 26, 3, 4, 2, 5, 1, 2, 3, 9, 2, 6, 3, 4, 3, 4, 2, 21, 2, 2, 6, 4, 1, 2, 2, 17, 3, 2, 1, 14, 1, 12, 10, 57, 5, 6, 1, 8, 3, 5, 2, 11, 8, 2, 3, 4, 2, 6, 2, 18, 1, 4, 1, 13, 10, 6, 3, 8, 8, 7, 7, 8, 9, 4

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OFFSET

2,5

LINKS

Table of n, a(n) for n=2..94.

EXAMPLE

2^6=64; the numbers 64-s(j) are 63,62,60,56,48,32, of which two are multiples of 6, so that a(6)=2.

MATHEMATICA

s[k_] := 2^(k - 1);

f[n_, k_] := If[Mod[s[n] - s[k], n] == 0, 1, 0];

t[n_] := Flatten[Table[f[n, k], {k, 1, n - 1}]]

a[n_] := Count[Flatten[t[n]], 1]