Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #15 Sep 02 2017 09:41:53
%S 1,1,1,1,1,1,1,1,1,1,3,1,3,1,1,1,8,1,11,1,1,2,20,1,1,2,1,1
%N Number of primitive sequences n = b_1 < b_2 < ... < b_t = A006255(n) such that b_1*b_2*...*b_t is a perfect square.
%C A primitive sequence is one such that no proper, nonempty subsequence has a product that is a perfect square.
%C Trivially, a(n) <= A259527(n). If A259527(n) = 1, then a(n) = 1.
%p For n = 22 the a(22) = 2 solutions are:
%p 22 * 24 * 33 = 132^2, and
%p 22 * 27 * 32 * 33 = 792^2.
%p Note that 22 * 24 * 25 * 33 = 660^2 is not a solution because the subsequence [25] has a square product.
%Y Cf. A006255, A259527.
%K nonn,more
%O 1,11
%A _Peter Kagey_, Aug 29 2017