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A212645 a(n) = number of excess prime divisors of A181800(n) (n-th 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 (4-2) = 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

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Last modified May 26 05:25 EDT 2019. Contains 323579 sequences. (Running on oeis4.)