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%I A369939 #9 Aug 07 2024 03:07:55
%S A369939 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,
%T A369939 28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,49,50,51,
%U A369939 52,53,54,55,56,57,58,59,60,61,62,63,65,66,67,68,69,70,71
%N A369939 Numbers whose maximal exponent in their prime factorization is a Fibonacci number.
%C A369939 First differs from its subsequence A115063 at n = 2448. a(2448) = 2592 = 2^5 * 3^4 is not a term of A115063.
%C A369939 First differs from A209061 at n = 62.
%C A369939 Numbers k such that A051903(k) is a Fibonacci number.
%C A369939 The asymptotic density of this sequence is 1/zeta(4) + Sum_{k>=5} (1/zeta(Fibonacci(k)+1) - 1/zeta(Fibonacci(k))) = 0.94462177878047854647... .
%H A369939 Amiram Eldar, <a href="/A369939/b369939.txt">Table of n, a(n) for n = 1..10000</a>
%t A369939 fibQ[n_] := Or @@ IntegerQ /@ Sqrt[5*n^2 + {-4, 4}];
%t A369939 Select[Range[100], fibQ[Max[FactorInteger[#][[;; , 2]]]] &]
%o A369939 (PARI) isfib(n) = issquare(5*n^2 - 4) || issquare(5*n^2 + 4);
%o A369939 is(n) = n == 1 || isfib(vecmax(factor(n)[, 2]));
%Y A369939 Cf. A000045, A013662, A051903, A209061.
%Y A369939 Subsequences: A005117, A062503, A062838, A113850, A115063.
%Y A369939 Similar sequences: A368714, A369937, A369938.
%K A369939 nonn,easy
%O A369939 1,2
%A A369939 _Amiram Eldar_, Feb 06 2024

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