A212639 Number of prime factors of A181800(n) (n-th powerful number that is the first integer of its prime signature), counted with multiplicity.

0, 2, 3, 4, 5, 4, 6, 5, 7, 6, 6, 8, 7, 7, 9, 8, 8, 6, 10, 9, 8, 9, 7, 11, 10, 9, 10, 8, 12, 11, 10, 8, 11, 9, 10, 13, 12, 11, 9, 12, 10, 11, 14, 13, 12, 10, 9, 13, 11, 12, 10, 15, 14, 13, 11, 8, 12, 10, 14, 12, 13, 11, 16, 15, 14, 12, 9, 13, 11, 15, 13, 14, 12

Offset: 1

Author

Matthew Vandermast, Jun 09 2012

Keywords

• nonn

Comments

Every nonnegative integer n appears A002865(n) times.

Examples

			72 (2^3*3^2, or 2*2*2*3*3) has a total of 5 prime factors when repetitions are counted.  Since 72 = A181800(8), a(8) = 5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Will Nicholes, List of prime signatures

Crossrefs

Cf. A181800, A001222, A212172, A212176, A212179, A212645.

Formula

a(n) = A001222(A181800(n)).