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

1,2

Comments

Every nonnegative integer n appears A002865(n) times.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Will Nicholes, List of prime signatures

Formula

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

Example

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.

Crossrefs

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

Sequence in context: A323161 A152739 A279614 * A212647 A303233 A137912

Adjacent sequences: A212636 A212637 A212638 * A212640 A212641 A212642

Keyword

nonn

Author

Matthew Vandermast, Jun 09 2012

Status

approved