A175130 Indices of Fibonacci numbers that are not cubefree.

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 125, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 250, 252, 258, 264, 270, 276, 282, 288, 294, 300, 306, 312, 318, 324

Offset: 1

Author

R. J. Mathar, Feb 16 2010

Keywords

• nonn

Comments

Supersequence of A037917.

Conjecture: all terms are multiples of 6 or 125. - Harvey P. Dale, Apr 28 2020

The conjecture is false. The counterexamples are 392, 784, 1183, 1210, .... . - Amiram Eldar, Oct 16 2023

Examples

			Fibonacci(125) = 5^3 * 3001 * 158414167964045700001 = A000045(125) is not cubefree, which adds 125 to the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..248
• Blair Kelly, Fibonacci factorizations.

Crossrefs

Cf. A000045, A010056, A037917, A046099, A134492, A212793.

Programs

Haskell

import Data.List (findIndices)
a175130 n = a175130_list !! (n-1)
a175130_list = map (+ 1) $ findIndices ((== 0) . a212793) $ tail a000045_list
-- Reinhard Zumkeller, May 27 2012

Mathematica

Select[Range[350],Max[FactorInteger[Fibonacci[#]][[All,2]]]>2&] (* Harvey P. Dale, Apr 28 2020 *)

PARI

is(n)=n>5 && vecmax(factor(fibonacci(n))[,2])>2 \\ Charles R Greathouse IV, Nov 07 2014

Formula

A000045 INTERSECT A046099.

A010056(a(n)) * (1 - A212793(a(n))) = 1. - Reinhard Zumkeller, May 27 2012