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

1,6

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).

Links

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

Will Nicholes, Prime Signatures

Formula

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

Example

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

Crossrefs

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

Sequence in context: A175044 A106149 A253607 * A257023 A238894 A054740

Adjacent sequences: A212176 A212177 A212178 * A212180 A212181 A212182

Keyword

nonn

Author

Matthew Vandermast, Jun 04 2012

Status

approved