A184221 a(n) = A184220(n)/A133150(n) unless A133150(n) = 0 in which case a(n) = 0.

0, 0, 0, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 7, 7, 1, 2, 1, 2, 1, 7, 7, 2, 1, 2, 1, 2, 7, 14, 1, 2, 1, 2, 1, 14, 7, 17, 1, 2, 1, 2, 17, 14, 1, 2, 1, 2, 23, 14, 7, 2, 1, 2, 17, 2, 7, 14, 1, 17, 1, 23, 1, 14, 7, 2, 1, 31, 1, 2, 7, 34, 1, 2, 1

Offset: 1

Author

Rémi Eismann, Jan 10 2011

Keywords

• nonn

Comments

a(n) is the "level" of squares (A000290).

The decomposition of squares into weight * level + gap is A000217(n) = A133150(n) * a(n) + A005408(n) if a(n) > 0.

A184220(n) = A000290(n) - A005408(n) if A000217(n) - A005408(n) > A005408(n), 0 otherwise.

Examples

			For n = 3 we have A133150(3) = 0, hence a(3) = 0.
For n = 5 we have A184220(5)/A133150(5) = 14 / 14 = 1, hence a(5) = 1.
For n = 25 we have A184220(25)/A133150(25) = 574 / 82 = 5, hence a(25) = 7.
		

Links

• Rémi Eismann, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, A005408, A133150, A184220, A118534, A117078, A117563, A001223.