A212647 a(n) = product of exponents in canonical prime factorization of A181800(n) (n-th powerful number that is the first integer of its prime signature); a(1) = 1 by convention.

1, 2, 3, 4, 5, 4, 6, 6, 7, 8, 9, 8, 10, 12, 9, 12, 15, 8, 10, 14, 16, 18, 12, 11, 16, 20, 21, 16, 12, 18, 24, 18, 24, 20, 25, 13, 20, 28, 24, 27, 24, 30, 14, 22, 32, 30, 27, 30, 28, 35, 32, 15, 24, 36, 36, 16, 36, 36, 33, 32, 40, 40, 16, 26, 40, 42, 24, 42, 45

Offset

1,2

Comments

The product of exponents in the canonical prime factorization of n, or A005361(n), is a function of the second signature of n (cf. A212172). Since A181800 consists of the first integer of each second signature, this sequence gives the value of A005361 for each second signature in order of its first appearance.

a(n) also gives the number of divisors of A212638(n), a permutation of A025487. Each positive integer n appears A001055(n) times in this sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Formula

a(n) = A005361(A181800(n)).

a(n) = A000005(A212638(n)).

Example

The product of the exponents in the prime factorization of 144 (2^4*3^2) is 4*2 = 8.  Since 144 = A181800(10), a(10) = 8.

Crossrefs

Cf. A005361, A181800, A212172, A212638.

Sequence in context: A152739 A279614 A212639 * A303233 A137912 A324196

Adjacent sequences: A212644 A212645 A212646 * A212648 A212649 A212650

Keyword

nonn

Author

Matthew Vandermast, Jun 09 2012

Status

approved