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

Author

Robert Price, Mar 07 2017

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

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

Formula

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

Extensions

More terms from Michel Marcus, Mar 11 2017