A212645 - OEIS

A212645

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

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

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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

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

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: A325980 A366122 A182718 * A364951 A364950 A100798

Adjacent sequences: A212642 A212643 A212644 * A212646 A212647 A212648

KEYWORD

nonn

AUTHOR

Matthew Vandermast, Jun 09 2012

STATUS

approved