A184831 a(n) = A184830(n)/A184829(n) unless A184829(n) = 0 in which case a(n) = 0.

0, 0, 1, 1, 1, 3, 1, 1, 3, 2, 5, 5, 3, 7, 1, 5, 9, 15, 3, 3, 13, 3, 15, 9, 1, 19, 2, 1, 9, 23, 1, 11, 1, 11, 9, 3, 33, 11, 35, 21, 7, 13, 41, 63, 25, 5, 45, 3, 49, 5, 1, 3, 55, 33, 1, 59, 9, 63, 27, 65, 11, 1, 3, 75, 45, 1, 79, 1, 5, 41, 85, 1, 1, 89, 5, 39, 93, 1, 57, 9

Offset: 1

Author

Rémi Eismann, Jan 23 2011

Keywords

• nonn

Comments

a(n) is the "level" of prime powers.

The decomposition of prime powers into weight * level + gap is A000961(n) = A184829(n) * a(n) + A057820(n) if a(n) > 0.

A184830(n) = A000961(n) - A057820(n) if A000961(n) - A057820(n) > A057820(n), 0 otherwise.

Examples

			For n = 1 we have A184829(1) = 0, hence a(1) = 0.
For n = 3 we have A184830(3)/A184829(3)= 2 / 2 = 1; hence a(3) = 1.
For n = 24 we have A184830(24)/A184829(24)= 45 / 5 = 9; hence a(24) = 9.
		

Links

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

Crossrefs

Cf. A000961, A057820, A184829, A184830, A117078, A117563, A001223, A118534.