A212638 - OEIS

%I #11 Jun 20 2019 17:51:19

%S 1,2,4,8,16,6,32,12,64,24,36,128,48,72,256,96,144,30,512,192,216,288,

%T 60,1024,384,432,576,120,2048,768,864,180,1152,240,1296,4096,1536,

%U 1728,360,2304,480,2592,8192,3072,3456,720,900,4608,960,5184,1080,16384

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

%C 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.

%C A permutation of A025487.

%H Amiram Eldar, <a href="/A212638/b212638.txt">Table of n, a(n) for n = 1..1000</a>

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

%e 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.

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

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

%K nonn

%O 1,2

%A _Matthew Vandermast_, Jun 05 2012