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Composite numbers n such that 8*n^2-2*n-1 divides the primitive part U(n) of Fibonacci(n).
2

%I #19 Apr 03 2023 10:36:11

%S 27,807,1707,2977,3027,3277,4717,5137,5677,5917,5967,6187,7087,7357,

%T 7597,7707,8217,9117,9297,9387,9667,9877,9927,9997,10387,11097,11647,

%U 11797,12727,13407,13867,15757,15987,16327,16507,16857,17347,17767,18237,18817,18997

%N Composite numbers n such that 8*n^2-2*n-1 divides the primitive part U(n) of Fibonacci(n).

%H Chris Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/xpage/FibonacciNumber.html">Fibonacci number</a>

%t lst = {1}; Do[f = Fibonacci[a]; Do[f = f/GCD[f, lst[[d]]], {d, Most[Divisors[a]]}]; AppendTo[lst, f], {a, 2, 19000}]; Flatten[Table[If[! PrimeQ[n] && Mod[lst[[n]], 8*n^2 - 2*n - 1] == 0, n, {}], {n, 19000}]] (* _Arkadiusz Wesolowski_, Dec 12 2011 *)

%Y Subsequence of A159259.

%Y Cf. A000045, A023172, A061446, A159231, A181890.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Apr 06 2009