A212179 Number of distinct prime factors of A181800(n) (n-th powerful number that is the first integer of its prime signature).

0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 3, 1, 2, 2, 2, 3, 1, 2, 2, 3, 2, 3, 2, 1, 2, 2, 3, 2, 3, 2, 1, 2, 2, 3, 3, 2, 3, 2, 3, 1, 2, 2, 3, 4, 2, 3, 2, 3, 2, 3, 1, 2, 2, 3, 4, 2, 3, 2, 3, 2, 3, 1, 2, 3, 2, 3, 4, 2, 3, 3, 2, 3, 2, 3, 1, 4

Offset: 1

Author

Matthew Vandermast, Jun 04 2012

Keywords

• nonn

Comments

Since each prime factor of A181800(n) divides A181800(n) at least twice, this is also the number of exponents > 2 in prime factorization of A181800(n).

Length of row A181800(n) of table A212171 equals a(n) for n > 1. Row A181800(n) of table A212172 has the same length when n > 1 (length = 1 if n = 1).

Examples

			72 (2^3*3^2) has 2 distinct prime factors. Since 72 = A181800(8), a(8) = 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Will Nicholes, Prime Signatures

Crossrefs

Cf. A181800, A001694, A025487, A212171, A212172, A212176.

Formula

a(n) = A001221(A181800(n)) = A056170(A181800(n)).