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

1,1

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..248

Blair Kelly, Fibonacci factorizations.

Formula

A000045 INTERSECT A046099.

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A315772 A121827 A126798 * A008458 A008588 A078596

Adjacent sequences: A175127 A175128 A175129 * A175131 A175132 A175133

Keyword

nonn

Author

R. J. Mathar, Feb 16 2010

Status

approved