%I #15 Mar 13 2020 16:55:52
%S 2,2,2,10,2,28,2,10,2,22,10,910,2,2,2,170,2,3458,2,110,2,46,10,910,2,
%T 2,2,290,2,9548,2,340,10,2,22,639730,2,2,2,4510,2,1204,10,230,2,94,2,
%U 216580,2,22,2,530,2,3458,22,580,2,118,2,18928910
%N Least positive integer k such that 3^n1 and k^n1 are relatively prime.
%C Note that (3^n1)^n1 is always relatively prime to 3^n1.
%C According to the conjecture given in A086892, a(n) = 2 infinitely often.
%C When n>1, a(n) = 2 if and only if A260119(n) = 3.
%e Since 3^51 = 242 and 2^51 = 31 are relatively prime, a(5) = 3.
%t Table[k = 1; While[! CoprimeQ[3^n  1, k^n  1], k++]; k, {n, 59}] (* _Michael De Vlieger_, Jan 27 2016 *)
%o (Sage)
%o def min_k(n):
%o g, k=2, 0
%o while g!=1:
%o k=k+1
%o g=gcd(3^n1, k^n1)
%o return k
%o print([min_k(n) for n in [1..60]])
%o (PARI) a(n) = {k=1; while( gcd(3^n1, k^n1)!=1, k++); k; }
%Y Cf. A086892, A260119.
%K nonn
%O 1,1
%A _Tom Edgar_, Jan 25 2016
