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.

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, 8192, 4, 2, 16, 2, 1, 65536, 64, 4, 2, 524288, 8, 1048576, 4, 4, 128, 8388608, 2, 1, 1, 8, 2, 67108864, 4, 2, 2, 4, 256, 536870912, 2, 2147483648, 2048, 2, 1, 1

Offset: 1

Author

Peter Kagey, Jun 29 2015

Keywords

• nonn

Comments

All terms are powers of 2.

Examples

			For a(20)=4 the solutions are:
s_0 = {20,24,30} with prod(s_0) = 120^2;
s_1 = {20,24,25,30} with prod(s_1) = 600^2;
s_2 = {20,21,24,27,28,30} with prod(s_2) = 15120^2;
s_3 = {20,21,24,25,27,28,30} with prod(s_3) = 75600^2.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006255, A260510.

Extensions

More terms from Alois P. Heinz, Jul 16 2015