%I #11 Jul 14 2019 08:22:00

%S 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,

%T 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,

%U 11,8,15,13,12,9,5,11,8,13,10,12,9,16,14,8,13,10

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

%C 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.

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

%H Amiram Eldar, <a href="/A212645/b212645.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%e 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.

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

%Y A rearrangement of A036042.

%K nonn

%O 1,3

%A _Matthew Vandermast_, Jun 09 2012