A328143 Number of sequences [(b_1, c_1),...,(b_t, c_t)] such that n = b_1 < b_2 < ... < b_t = A328045(n), all c_i are positive integers less than 4, and b_1^c_1*b_2^c_2*...*b_t^c_t is a fourth power.

3, 3, 2, 2, 1, 12, 2, 12, 12, 1, 12, 192, 12, 768, 12, 12, 3, 12288, 12, 49152, 2, 6, 48

Offset: 0

Author

Peter Kagey, Oct 04 2019

Keywords

• nonn
• more

Comments

When does a(n) = 3*4^A260510(n)? It does for n = 0, 1, 5, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, ...

a(n) = 1 if n is square but not a fourth power.

a(k^4) = 3.

a(24) = 2, a(25) = 1, a(26) = 48, a(27) = 3, and a(28) = 2.

Examples

			For n = 21 the a(21) = 6 solutions are
21^2 *               27^2 * 28^2 =  126^4,
21^3 * 24^2 *        27^1 * 28^1 =  252^4,
21^2 *        25^2 * 27^2 * 28^2 =  630^4,
21^3 * 24^2 * 25^2 * 27^1 * 28^1 = 1260^4,
21^1 * 24^2 *        27^3 * 28^3 = 1512^4, and
21^1 * 24^2 * 25^2 * 27^3 * 28^3 = 7560^4.
		

Crossrefs

Cf. A006255, A260510, A277494, A328045.

A259527 is the analog for squares.