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A259527 a(n) gives the number of sequences n = b_1 < b_2 < ... < b_t = A006255(n) such that b_1*b_2*...*b_t is a perfect square.

%I A259527 #25 Mar 24 2017 00:47:58
%S A259527 1,2,2,1,2,2,2,2,1,2,8,2,16,2,2,1,64,2,128,4,2,4,512,2,1,4,1,2,8192,2,
%T A259527 8192,4,2,16,2,1,65536,64,4,2,524288,8,1048576,4,4,128,8388608,2,1,1,
%U A259527 8,2,67108864,4,2,2,4,256,536870912,2,2147483648,2048,2,1,1
%N A259527 a(n) gives the number of sequences n = b_1 < b_2 < ... < b_t = A006255(n) such that b_1*b_2*...*b_t is a perfect square.
%C A259527 All terms are powers of 2.
%H A259527 Peter Kagey, <a href="/A259527/b259527.txt">Table of n, a(n) for n = 1..1000</a>
%e A259527 For a(20)=4 the solutions are:
%e A259527 s_0 = {20,24,30} with prod(s_0) = 120^2;
%e A259527 s_1 = {20,24,25,30} with prod(s_1) = 600^2;
%e A259527 s_2 = {20,21,24,27,28,30} with prod(s_2) = 15120^2;
%e A259527 s_3 = {20,21,24,25,27,28,30} with prod(s_3) = 75600^2.
%Y A259527 Cf. A006255, A260510.
%K A259527 nonn
%O A259527 1,2
%A A259527 _Peter Kagey_, Jun 29 2015
%E A259527 More terms from _Alois P. Heinz_, Jul 16 2015