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A270839 Integers k such that (A003266(k)/A000045(k-1)) is not divisible by k.

%I A270839 #26 Apr 01 2021 08:23:43
%S A270839 2,3,4,7,9,11,19,23,31,43,59,67,71,79,83,103,127,131,163,167,179,191,
%T A270839 223,227,239,251,271,283,311,359,367,379,383,419,431,439,443,463,467,
%U A270839 479,487,491,499,503,523,547,571,587,599,607,631,643,647,659,683,719,727,739,751,787,823,827,839
%N A270839 Integers k such that (A003266(k)/A000045(k-1)) is not divisible by k.
%C A270839 A270777 is a subsequence.
%C A270839 It appears that this sequence generates prime numbers except 4 and 9. [Verified for the first 500 terms. - _Amiram Eldar_, Apr 01 2021]
%H A270839 Amiram Eldar, <a href="/A270839/b270839.txt">Table of n, a(n) for n = 1..500</a>
%e A270839 3 is a term because 1*2 is not divisible by 3.
%e A270839 7 is a term because 1*1*2*3*5*13 is not divisible by 7.
%t A270839 Select[Range[2, 840], ! Divisible[Fibonorial@ #/Fibonacci[# - 1], #] &] (* Version 10, or *) Select[Range[2, 840], ! Divisible[Product[Fibonacci@ k, {k, #}]/Fibonacci[# - 1], #] &] (* _Michael De Vlieger_, Mar 24 2016 *)
%o A270839 (PARI) t(n) = fibonacci(n) * prod(k=1, n-2, Mod(fibonacci(k), n));
%o A270839 for(n=2, 1e3, if(lift(t(n)) != 0, print1(n, ", ")));
%Y A270839 Cf. A000045, A000057, A003266, A270777.
%K A270839 nonn
%O A270839 1,1
%A A270839 _Altug Alkan_, Mar 23 2016
%E A270839 Offset corrected by _Amiram Eldar_, Apr 01 2021