A179621 a(n) = A179620(n)/A130882(n) unless A130882(n) = 0 in which case a(n) = 0.

0, 1, 1, 4, 2, 2, 1, 7, 2, 4, 1, 10, 5, 1, 12, 5, 13, 2, 7, 1, 16, 11, 17, 2, 1, 19, 2, 10, 1, 22, 11, 1, 24, 7, 25, 10, 1, 27, 11, 28, 14, 2, 1, 31, 21, 32, 16, 1, 34, 17, 14, 1, 37, 25, 38, 19, 1, 40, 20, 1, 42, 17, 43, 2, 1, 45, 13, 46, 31, 47, 2, 1, 49, 14, 25, 1, 52, 26, 2, 1

Offset: 1

Author

Rémi Eismann, Jan 09 2011

Keywords

• nonn

Comments

a(n) is the "level" of composite numbers.

The decomposition of composite numbers into weight * level + gap is A002808(n) = A130882(n) * a(n) + A073783(n) if a(n) > 0.

A179620(n) = A002808(n) - A073783(n) if A002808(n) - A073783(n) > A073783(n), 0 otherwise.

Examples

			For n = 1 we have A130882(1) = 0, hence a(1) = 0.
For n = 3 we have A179620(3)/A130882(3)= 7 / 7 = 1; hence a(3) = 1.
For n = 24 we have A179620(24)/A130882(24)= 34 / 17 = 2; hence a(24) = 2.
		

Links

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

Crossrefs

Cf. A002808, A073783, A130882, A179620, A117078, A117563, A001223, A118534.