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%I #9 Mar 20 2016 12:58:13
%S 2,3,4,6,7,22,23,42,43,66,67,82,83,102,103,126,127,162,163,166,167,
%T 222,223,226,227,282,283,366,367,382,383,442,443,462,463,466,467,486,
%U 487,502,503,522,523,546,547,586,587,606,607,642,643,646,647,682,683,726,727,786,787
%N Integers n such that A003266(n) is not divisible by n*(n+1)/2.
%C This sequence contains primes dividing all Fibonacci sequences.
%e 6 is a term because (1*1*2*3*5*8) is not divisible by (1+2+3+4+5+6).
%e 5 is not a term because (1*1*2*3*5) is divisible by (1+2+3+4+5).
%t nn = 800; Function[k, Select[Range@ nn, ! Divisible[k[[#]], # (# + 1)/2] &]]@ FoldList[Times, Array[Fibonacci@ # &, nn]] (* _Michael De Vlieger_, Mar 19 2016 *)
%o (PARI) a(n) = prod(k=1, n, fibonacci(k));
%o for(n=1, 1e3, if(a(n) % (n*(n+1)/2) != 0, print1(n, ", ")));
%Y Cf. A000040, A000057, A003266.
%K nonn
%O 1,1
%A _Altug Alkan_, Mar 17 2016