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

1,11

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.

Links

Table of n, a(n) for n=1..28.

Maple

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.

Sequence in context: A274613 A066975 A355879 * A098877 A225212 A091088

Adjacent sequences: A291631 A291632 A291633 * A291635 A291636 A291637

Keyword

nonn,more

Author

Peter Kagey, Aug 29 2017

Status

approved