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

1,1

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)

Formula

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

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 *)

Prog

(PARI) for(k=1, 1e3, if(!issquarefree(3^k-1), print1(k, ", ")))
(Magma) [n: n in [1..110]| not IsSquarefree(3^n-1)]; // Vincenzo Librandi, Oct 25 2014

Crossrefs

Cf. A024023, A049094, A065502.

Cf. A005117, A013929, A283620.

Sequence in context: A047434 A062414 A324694 * A065502 A077255 A262439

Adjacent sequences: A249022 A249023 A249024 * A249026 A249027 A249028

Keyword

nonn

Author

Felix Fröhlich, Oct 19 2014

Status

approved