A270470 Integers n such that A001654(n) is divisible by n*(n+1)/2.

1, 3, 10, 23, 24, 47, 60, 107, 108, 167, 180, 240, 250, 323, 383, 503, 540, 575, 600, 647, 660, 683, 768, 863, 1008, 1103, 1200, 1223, 1320, 1367, 1620, 1728, 1800, 1860, 2160, 2207, 2447, 2520, 2687, 2688, 2736, 3000, 3023, 3060, 3300, 3360, 3527, 3528, 3744, 3863, 3888, 4200, 4703, 4800

Offset

1,2

Comments

Odd terms of this sequence are prime most of the time. Odd composite terms of this sequence are 1, 323, 575, 6479, 7055, ...

Links

Table of n, a(n) for n=1..54.

Example

3 is a term because (1^2 + 1^2 + 2^2) / (1 + 2 + 3) = 1.
10 is a term because (1^2 + 1^2 + 2^2 + 3^2 + 5^2 + 8^2 + 13^2 + 21^2 + 34^2 + 55^2) / (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) = 89.

Mathematica

nn = 4800; Function[k, Select[Range@ nn, Divisible[k[[# + 1]], # (# + 1)/2] &]]@ LinearRecurrence[{2, 2, -1}, {0, 1, 2}, nn + 1] (* Michael De Vlieger, Mar 19 2016, after Vladimir Joseph Stephan Orlovsky at A001654 *)

Prog

(PARI) a(n) = fibonacci(n)*fibonacci(n+1);
for(n=1, 1e4, if(a(n) % (n*(n+1)/2) ==0, print1(n, ", ")));

Crossrefs

Cf. A000217, A001654.

Sequence in context: A171686 A027164 A292921 * A166119 A041403 A077126

Adjacent sequences: A270467 A270468 A270469 * A270471 A270472 A270473

Keyword

nonn

Author

Altug Alkan, Mar 17 2016

Status

approved