A184751 a(n) = A184750(n)/A133151(n) unless A133151(n) = 0 in which case a(n) = 0.

0, 0, 0, 0, 1, 1, 2, 1, 1, 3, 2, 1, 3, 4, 4, 3, 1, 2, 6, 1, 1, 9, 8, 1, 3, 2, 2, 3, 1, 4, 12, 1, 1, 6, 2, 1, 3, 16, 16, 9, 1, 2, 19, 1, 1, 12, 4, 19, 9, 2, 2, 3, 1, 8, 24, 1, 1, 18, 23, 1, 3, 19, 4, 3, 1, 23, 19, 1, 1, 32, 16, 1, 3, 2, 2, 27, 1, 4, 12, 1, 19, 23

Offset: 1

Author

Rémi Eismann, Jan 21 2011

Keywords

• nonn

Comments

a(n) is the "level" of pentagonal numbers (A000326).

The decomposition of pentagonal numbers into weight * level + gap is A000326(n) = A133151(n) * a(n) + A016777(n) if a(n) > 0.

A184750(n) = A000326(n) - A016777(n) if A000326(n) - A016777(n) > A016777(n), 0 otherwise.

Examples

			For n = 3 we have A133151(3) = 0, hence a(3) = 0.
For n = 5 we have A184750(5)/A133151(5) = 19 / 19 = 1, hence a(5) = 1.
For n = 25 we have A184750(25)/A133151(25) = 849 / 283 = 5, hence a(25) = 3.
		

Links

• Rémi Eismann, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000326, A016777, A133151, A184750, A117078, A117563, A001223, A118534.