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

Author

Amiram Eldar, Feb 06 2024

Keywords

• nonn
• easy

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))) = 0.94462177878047854647... .

Links

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

Crossrefs

Cf. A000045, A013662, A051903, A209061.

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

Similar sequences: A368714, A369937, A369938.

Programs

Mathematica

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

PARI

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