login
A212179
Number of distinct prime factors of A181800(n) (n-th powerful number that is the first integer of its prime signature).
4
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
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
KEYWORD
nonn
AUTHOR
Matthew Vandermast, Jun 04 2012
STATUS
approved