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Numbers k such that 12k does not divide Fibonacci(12k).
3

%I #9 Jun 08 2021 02:17:41

%S 7,11,13,17,19,21,22,23,26,29,31,33,34,35,37,38,39,41,43,44,47,49,52,

%T 53,58,59,61,62,63,65,66,67,68,69,71,73,74,76,77,78,79,82,83,85,86,87,

%U 88,89,91,93,94,95,97,99,101,103,104,105,106,107,109,111,113,115,116,117

%N Numbers k such that 12k does not divide Fibonacci(12k).

%C Complement of A072378 = {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 24, 25, 27, ...} (numbers k such that 12k divides Fibonacci(12k)). It appears that {a(n)} includes all powers p^k for prime p > 5 and integer k > 0.

%H Seiichi Manyama, <a href="/A128974/b128974.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[ Range[400], !IntegerQ[ Fibonacci[ 12# ] / (12#) ] & ]

%Y Cf. A072378 (numbers k such that 12k divides Fibonacci(12k)).

%Y Cf. A023172 (numbers k such that k divides Fibonacci(k)).

%K nonn

%O 1,1

%A _Alexander Adamchuk_, May 11 2007