A369939 Numbers whose maximal exponent in their prime factorization is a Fibonacci number.

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, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71

Offset

1,2

Comments

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

First differs from A209061 at n = 62.

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

The asymptotic density of this sequence is 1/zeta(4) + Sum_{k>=5} (1/zeta(Fibonacci(k)+1) - 1/zeta(Fibonacci(k)+1)) = 0.94462177878047854647... .

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

fibQ[n_] := Or @@ IntegerQ /@ Sqrt[5*n^2 + {-4, 4}];
Select[Range[100], fibQ[Max[FactorInteger[#][[;; , 2]]]] &]

Prog

(PARI) isfib(n) = issquare(5*n^2 - 4) || issquare(5*n^2 + 4);
is(n) = n == 1 || isfib(vecmax(factor(n)[, 2]));

Crossrefs

Cf. A000045, A013662, A051903, A209061.

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

Similar sequences: A368714, A369937, A369938.

Sequence in context: A140823 A209061 A115063 * A178210 A013938 A339889

Adjacent sequences: A369936 A369937 A369938 * A369940 A369941 A369942

Keyword

nonn,easy

Author

Amiram Eldar, Feb 06 2024

Status

approved