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

0,1

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.

Links

Table of n, a(n) for n=0..22.

Example

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.

Sequence in context: A308725 A202691 A374410 * A278402 A276415 A309262

Adjacent sequences: A328140 A328141 A328142 * A328144 A328145 A328146

Keyword

nonn,more

Author

Peter Kagey, Oct 04 2019

Status

approved