A291634 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.

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

Offset: 1

Author

Peter Kagey, Aug 29 2017

Keywords

• nonn
• more

Comments

A primitive sequence is one such that no proper, nonempty subsequence has a product that is a perfect square.

Trivially, a(n) <= A259527(n). If A259527(n) = 1, then a(n) = 1.

Examples

			For n = 22 the a(22) = 2 solutions are:
22 * 24 * 33 = 132^2, and
22 * 27 * 32 * 33 = 792^2.
Note that 22 * 24 * 25 * 33 = 660^2 is not a solution because the subsequence [25] has a square product.
		

Crossrefs

Cf. A006255, A259527.