A212645 a(n) = number of excess prime divisors of A181800(n) (n-th powerful number that is the first integer of its prime signature).

0, 1, 2, 3, 4, 2, 5, 3, 6, 4, 4, 7, 5, 5, 8, 6, 6, 3, 9, 7, 6, 7, 4, 10, 8, 7, 8, 5, 11, 9, 8, 5, 9, 6, 8, 12, 10, 9, 6, 10, 7, 9, 13, 11, 10, 7, 6, 11, 8, 10, 7, 14, 12, 11, 8, 4, 10, 7, 12, 9, 11, 8, 15, 13, 12, 9, 5, 11, 8, 13, 10, 12, 9, 16, 14, 8, 13, 10

Offset: 1

Author

Matthew Vandermast, Jun 09 2012

Keywords

• nonn

Comments

The excess of n, or A046660(n), is a function of the second signature of n (cf. A212172). Since A181800 gives the first integer of each second signature, this sequence gives the value of A046660 for each second signature in order of its first appearance. Each nonnegative integer n occurs A000041(n) times in the sequence.

a(n) is also the number of prime factors of A212638(n), counted with multiplicity.

Examples

			36 (2^2*3^2, or 2*2*3*3) has 4 prime factors when repetitions are counted, but only 2 distinct prime factors.  Therefore, its "excess" as defined in A046660 is (4-2) = 2.  Since 36 = A181800(6), a(6) = 2.
		

Links

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

Crossrefs

Cf. A046660, A181800, A212172, A212176, A212179, A212638, A212639, A212647.

A rearrangement of A036042.

Formula

a(n) = A046660(A181800(n)) = A212639(n)-A212179(n).

a(n) = A001222(A212638(n)).