

A212645


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


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


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.


LINKS

Table of n, a(n) for n=1..78.


FORMULA

a(n) = A046660(A181800(n)) = A212639(n)A212179(n).
a(n) = A001222(A212638(n)).


EXAMPLE

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 (42) = 2. Since 36 = A181800(6), a(6) = 2.


CROSSREFS

Cf. A046660, A181800, A212172, A212176, A212179, A212638, A212639, A212647.
A rearrangement of A036042.
Sequence in context: A075994 A305893 A182718 * A100798 A302785 A319825
Adjacent sequences: A212642 A212643 A212644 * A212646 A212647 A212648


KEYWORD

nonn


AUTHOR

Matthew Vandermast, Jun 09 2012


STATUS

approved



