A369939 - OEIS

%I #9 Aug 07 2024 03:07:55

%S 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 28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,49,50,51,

%U 52,53,54,55,56,57,58,59,60,61,62,63,65,66,67,68,69,70,71

%N Numbers whose maximal exponent in their prime factorization is a Fibonacci number.

%C First differs from its subsequence A115063 at n = 2448. a(2448) = 2592 = 2^5 * 3^4 is not a term of A115063.

%C First differs from A209061 at n = 62.

%C Numbers k such that A051903(k) is a Fibonacci number.

%C 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 Amiram Eldar, <a href="/A369939/b369939.txt">Table of n, a(n) for n = 1..10000</a>

%t fibQ[n_] := Or @@ IntegerQ /@ Sqrt[5*n^2 + {-4, 4}];

%t Select[Range[100], fibQ[Max[FactorInteger[#][[;; , 2]]]] &]

%o (PARI) isfib(n) = issquare(5*n^2 - 4) || issquare(5*n^2 + 4);

%o is(n) = n == 1 || isfib(vecmax(factor(n)[, 2]));

%Y Cf. A000045, A013662, A051903, A209061.

%Y Subsequences: A005117, A062503, A062838, A113850, A115063.

%Y Similar sequences: A368714, A369937, A369938.

%K nonn,easy

%O 1,2

%A _Amiram Eldar_, Feb 06 2024