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A249025 Numbers k such that 3^k - 1 is not squarefree. 4
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 (list; graph; refs; listen; history; text; internal format)
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

Michel Marcus, Table of n, a(n) for n = 1..121

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

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Last modified March 22 17:25 EDT 2019. Contains 321422 sequences. (Running on oeis4.)