A283454 The square root of the smallest square referenced in A249025 (Numbers k such that 3^k - 1 is not squarefree).

2, 2, 11, 2, 2, 2, 2, 2, 11, 2, 2, 2, 2, 2, 11, 2, 2, 2, 2, 2, 11, 2, 2, 13, 2, 2, 2, 11, 2, 2, 2, 2, 2, 11, 2, 2, 2, 2, 2, 11, 2, 2, 2, 2, 2, 11, 2, 2, 2, 2, 2, 11, 2, 2, 2, 2, 2, 11, 2, 2, 2, 2, 2, 11, 2, 2, 2, 2, 2, 11, 2, 13, 2, 2, 2, 2, 11, 2, 2, 2, 2, 2, 11

Offset

1,1

Comments

The terms are the smallest prime whose square divides 3^k-1, when it is not squarefree.

Links

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

Formula

a(n) = A249739(A024023(A249025(n))). - Amiram Eldar, Feb 12 2021

Example

A249025(3)=5, 3^5-1 = 242 = 2*11*11. 242 is not squarefree the square being 11*11 = 121, the root being 11.

Mathematica

p[n_] := If[(f = Select[FactorInteger[n], Last[#] > 1 &]) == {}, 1, f[[1, 1]]]; p /@ Select[3^Range[100] - 1, !SquareFreeQ[#] &] (* Amiram Eldar, Feb 12 2021 *)

Prog

(PARI) lista(nn) = {for (n=1, nn, if (!issquarefree(k = 3^n-1), f = factor(k/core(k)); vsq = select(x->((x%2) == 0), f[, 2], 1); print1(f[vsq[1], 1], ", "); ); ); } \\ Michel Marcus, Mar 11 2017

Crossrefs

Cf. A024023, A046027, A249025, A249739, A283453.

Sequence in context: A081088 A236369 A001038 * A027623 A037234 A141651

Adjacent sequences: A283451 A283452 A283453 * A283455 A283456 A283457

Keyword

nonn

Author

Robert Price, Mar 07 2017

Extensions

More terms from Michel Marcus, Mar 11 2017

Status

approved