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

Author

Altug Alkan, Mar 17 2016

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A000217, A001654.

Programs

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 *)

PARI

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