A133180 a(n) = (Sum_{k=1..A047380(n)} k^6) / (Sum_{k=1..A047380(n)} k^2).

1, 13, 163, 373, 2191, 3433, 7411, 10363, 24583, 31591, 49981, 61723, 109513, 130351, 180793, 210901, 324013, 370273, 477463, 539041, 759811, 846613, 1042303, 1151983, 1533331, 1679323, 2002321, 2180263, 2785693, 3013051, 3509221

Offset: 1

Author

Artur Jasinski, Oct 10 2007

Keywords

• nonn
• easy

Comments

A000540(n) is divisible by A000330(n) if and only if n is congruent to {1,2,4,5} mod 7 (see A047380).

This sequence is the union of A134158 and A134159 and A134160 and A134161.

Crossrefs

Cf. A000330, A000540, A047380, A119617, A134153, A134154, A134158, A134159, A134160, A134161.

Programs

Mathematica

a = {}; Do[j = Sum[k^6, {k, 1, n}]/Sum[k^2, {k, 1, n}]; If[IntegerQ[j], AppendTo[a, j]], {n, 1, 100}] ; a (*Artur Jasinski*)
Select[Table[Sum[k^6,{k,n}]/Sum[k^2,{k,n}],{n,100}],IntegerQ] (* Harvey P. Dale, Nov 26 2019 *)

Formula

a(n) = A000540(A047380(n)) / A000330(A047380(n)). - Jason Yuen, Sep 23 2024

Extensions

Offset corrected by Jason Yuen, Sep 23 2024