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A206827 Number of solutions (n,k) of s(k)=s(n) (mod n), where 1<=k<n and s(k)=k(k+1)(2k+1)/6. 4
1, 1, 1, 2, 2, 2, 1, 1, 3, 2, 2, 2, 3, 3, 1, 2, 1, 2, 3, 3, 3, 2, 1, 2, 3, 1, 3, 2, 3, 2, 1, 3, 3, 8, 1, 2, 3, 3, 3, 2, 4, 2, 3, 3, 3, 2, 2, 2, 3, 3, 3, 2, 2, 8, 3, 3, 3, 2, 2, 2, 3, 3, 1, 8, 3, 2, 3, 3, 9, 2, 1, 2, 3, 3, 3, 8, 2, 2, 3, 1, 3, 2, 4, 8, 3, 3, 3, 2, 5, 8, 3, 3, 3, 8, 2, 2, 3, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,4

COMMENTS

For a guide to related sequences, see A206588.

LINKS

Table of n, a(n) for n=2..100.

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) (2 k + 1)/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}]  (* A206827 *)

CROSSREFS

Cf. A206588.

Sequence in context: A282011 A245514 A104754 * A098593 A144431 A053821

Adjacent sequences:  A206824 A206825 A206826 * A206828 A206829 A206830

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 15 2012

STATUS

approved

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Last modified May 26 00:02 EDT 2020. Contains 334612 sequences. (Running on oeis4.)