A212638 a(n) = n-th powerful number that is the first integer of its prime signature, divided by its largest squarefree divisor: A003557(A181800(n)).

1, 2, 4, 8, 16, 6, 32, 12, 64, 24, 36, 128, 48, 72, 256, 96, 144, 30, 512, 192, 216, 288, 60, 1024, 384, 432, 576, 120, 2048, 768, 864, 180, 1152, 240, 1296, 4096, 1536, 1728, 360, 2304, 480, 2592, 8192, 3072, 3456, 720, 900, 4608, 960, 5184, 1080, 16384

Offset: 1

Author

Matthew Vandermast, Jun 05 2012

Keywords

• nonn

Comments

The number of second signatures represented by the divisors of A181800(n) equals the number of prime signatures represented among the divisors of a(n). Cf. A212172, A212644.

A permutation of A025487.

Examples

			6 (whose prime factorization is 2*3) is the largest squarefree divisor of 144 (whose prime factorization is 2^4*3^2). Since 144 = A181800(10), and 144/6 = 24, a(10) = 24.
		

Links

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

Crossrefs

Cf. A003557, A007947, A085082, A181800, A212172, A212642, A212644.

Other permutations of A025487 include A036035, A059901, A063008, A077569, A085988, A086141, A087443, A108951, A181821, A181822.

Formula

a(n) = A003557(A181800(n)).