A270470 - OEIS

%I #9 Mar 20 2016 12:57:48

%S 1,3,10,23,24,47,60,107,108,167,180,240,250,323,383,503,540,575,600,

%T 647,660,683,768,863,1008,1103,1200,1223,1320,1367,1620,1728,1800,

%U 1860,2160,2207,2447,2520,2687,2688,2736,3000,3023,3060,3300,3360,3527,3528,3744,3863,3888,4200,4703,4800

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

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

%e 3 is a term because (1^2 + 1^2 + 2^2) / (1 + 2 + 3) = 1.

%e 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.

%t 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 *)

%o (PARI) a(n) = fibonacci(n)*fibonacci(n+1);

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

%Y Cf. A000217, A001654.

%K nonn

%O 1,2

%A _Altug Alkan_, Mar 17 2016