A249025 Numbers k such that 3^k - 1 is not squarefree.

2, 4, 5, 6, 8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 25, 26, 28, 30, 32, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 52, 54, 55, 56, 58, 60, 62, 64, 65, 66, 68, 70, 72, 74, 75, 76, 78, 80, 82, 84, 85, 86, 88, 90, 92, 94, 95, 96, 98, 100, 102, 104, 105, 106

Offset: 1

Author

Felix Fröhlich, Oct 19 2014

Keywords

• nonn

Comments

All even numbers are present (odd square - 1 == 0 mod 4). All multiples of 5 are present, since we can factorize 3^5k - 1 as (3^5-1)*[3^5(k-1) + ... + 1], and 3^5-1=121. Similarly all multiples of 39 are present since 3^39-1 = 405255515301=3^2*7*13^2*41^2*22643. - Jon Perry, Nov 09 2014

All multiples of positive members of A283620. - Robert Israel, Mar 16 2017

Links

• Amiram Eldar, Table of n, a(n) for n = 1..407 (terms 1..121 from Michel Marcus)

Crossrefs

Cf. A024023, A049094, A065502.

Cf. A005117, A013929, A283620.

Programs

Magma

[n: n in [1..110]| not IsSquarefree(3^n-1)]; // Vincenzo Librandi, Oct 25 2014

Maple

select(t -> igcd(t,10) > 1 or not numtheory:-issqrfree(3^t-1), [$1..150]); # Robert Israel, Mar 16 2017

Mathematica

Select[Range[120], ! SquareFreeQ[3^# - 1] &] (* Vincenzo Librandi, Oct 25 2014 *)

PARI

for(k=1, 1e3, if(!issquarefree(3^k-1), print1(k, ", ")))

Formula

A107078(A024023(n)) --> a(n) = log_3(A024023(n)).