A206826 Number of solutions (n,k) of s(k)=s(n) (mod n), where 1<=k<n and s(k)=k(k+1)(k+2)/6.

0, 2, 1, 2, 1, 2, 1, 2, 3, 2, 2, 2, 3, 4, 1, 2, 1, 2, 6, 3, 3, 2, 4, 2, 3, 2, 6, 2, 5, 2, 1, 3, 3, 8, 3, 2, 3, 4, 6, 2, 3, 2, 6, 3, 3, 2, 2, 2, 3, 5, 6, 2, 1, 8, 6, 5, 3, 2, 8, 2, 3, 5, 1, 8, 5, 2, 6, 4, 12, 2, 2, 2, 3, 3, 6, 8, 4, 2, 6, 2, 3, 2, 8, 8, 3, 3, 6, 2, 5, 8, 6, 4, 3, 8, 2, 2, 3, 4, 6

Offset

1,2

Links

Table of n, a(n) for n=1..99.

Example

5 divides exactly two of the numbers s(n)-s(k) for k=1,2,3,4, so that a(5)=2.

Mathematica

s[k_] := k (k + 1) (k + 2)/6;
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]
Table[a[n], {n, 2, 120}]  (* A206826 *)

Crossrefs

Cf. A206590.

Sequence in context: A254575 A355402 A275344 * A175835 A123738 A194511

Adjacent sequences: A206823 A206824 A206825 * A206827 A206828 A206829

Keyword

nonn

Author

Clark Kimberling, Feb 12 2012

Status

approved