A074214 - OEIS

A074214

Integers m such that F(m) and F(2m) have the same largest prime factor where F(k) denotes the k-th Fibonacci number.

3, 15, 21, 23, 25, 29, 33, 35, 39, 43, 45, 51, 55, 59, 63, 65, 75, 82, 83, 85, 87, 93, 99, 105, 107, 109, 111, 115, 119, 123, 125, 127, 131, 132, 133, 135, 137, 139, 142, 143, 145, 147, 151, 153, 158, 161, 166, 171, 173, 175, 179, 181, 183, 185, 187, 189, 191

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OFFSET

1,1

COMMENTS

Why are even values rare? (First one is 82.)

LINKS

Michel Marcus, Table of n, a(n) for n = 1..225

EXAMPLE

F(15) = 610 = 2*5*61 and F(30) = 832040 = 2^3*5*11*31*61 hence 15 is in the sequence.

MATHEMATICA

Select[Range[3, 200], FactorInteger[Fibonacci[#]][[-1, 1]]==FactorInteger[ Fibonacci[2#]][[-1, 1]]&] (* Harvey P. Dale, Sep 04 2018 *)

PROG