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

Author

Matthew Vandermast, Jun 09 2012

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A005361, A181800, A212172, A212638.

Formula

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

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