A283454 - OEIS

%I #27 Feb 12 2021 04:07:15

%S 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,

%T 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,

%U 11,2,2,2,2,2,11,2,13,2,2,2,2,11,2,2,2,2,2,11

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

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

%H Amiram Eldar, <a href="/A283454/b283454.txt">Table of n, a(n) for n = 1..407</a> (terms 1..121 from Michel Marcus)

%F a(n) = A249739(A024023(A249025(n))). - _Amiram Eldar_, Feb 12 2021

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

%t 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 *)

%o (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

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

%K nonn

%O 1,1

%A _Robert Price_, Mar 07 2017

%E More terms from _Michel Marcus_, Mar 11 2017