A280149 - OEIS

A280149

Numbers k such that 3^k - 2^k is not squarefree.

10, 11, 20, 22, 30, 33, 40, 42, 44, 50, 52, 55, 57, 60, 66, 70, 77, 80, 84, 88, 90, 99, 100, 104, 110, 114, 120, 121, 126, 130, 132, 140, 143, 150, 154, 156, 160, 165, 168, 170, 171, 176, 180, 187, 190, 198, 200, 203, 208, 209, 210, 220, 228, 230, 231, 240, 242, 250, 252, 253, 260, 264, 270, 272, 275, 280, 285

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OFFSET

1,1

COMMENTS

Primitive members (not multiples of earlier terms) are 10, 11, 42, 52, 57, 203, 272, 497, .... - Juri-Stepan Gerasimov and Charles R Greathouse IV, Dec 27 2016

From Robert Israel, Dec 27 2016: (Start)

Numbers divisible by the order of 3/2 mod p^2 for some prime p > 3.

Includes numbers divisible by p^2-p for some prime p > 3.

If k is a member, then so are all multiples of k. (End)

LINKS

Charles R Greathouse IV and Amiram Eldar, Table of n, a(n) for n = 1..134 (terms 1..127 from Charles R Greathouse IV)

EXAMPLE

10 is in this sequence because 3^10 - 2^10 = 58025 = 5^2*11*211.

MATHEMATICA

Select[Range@ 120, ! SquareFreeQ[3^# - 2^#] &] (* Michael De Vlieger, Dec 27 2016 *)

PROG

(Magma) [n: n in [1..156] | not IsSquarefree(3^n-2^n)];