A283453 The smallest square referenced in A249025 (Numbers k such that 3^k - 1 is not squarefree).

4, 4, 121, 4, 4, 4, 4, 4, 121, 4, 4, 4, 4, 4, 121, 4, 4, 4, 4, 4, 121, 4, 4, 169, 4, 4, 4, 121, 4, 4, 4, 4, 4, 121, 4, 4, 4, 4, 4, 121, 4, 4, 4, 4, 4, 121, 4, 4, 4, 4, 4, 121, 4, 4, 4, 4, 4, 121, 4, 4, 4, 4, 4, 121, 4, 4, 4, 4, 4, 121, 4, 169, 4, 4, 4, 4, 121

Offset: 1

Author

Robert Price, Mar 07 2017

Keywords

• nonn

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..407

Crossrefs

Cf. A249025, A283454.

Programs

Mathematica

psq[n_] := If[(f = Select[FactorInteger[n], Last[#] > 1 &]) == {}, 1, f[[1, 1]]^2]; psq /@ 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]^2, ", ");););} \\ Michel Marcus, Mar 11 2017

Formula

a(n) = A283454(n)^2. - Amiram Eldar, Feb 12 2021

Extensions

More terms from Michel Marcus, Mar 11 2017