A077569 -id:A077569 - cp's OEIS frontend

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

Matthew Vandermast, Jun 05 2012

nonn

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.

			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.

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

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

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

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

A131997 Array read by rows in which the n-th row contains odd numbers of all possible prime signatures with n divisors.

Original entry on oeis.org

1, 3, 9, 27, 15, 81, 243, 45, 729, 2187, 135, 105, 6561, 225, 19683, 405, 59049, 177147, 1215, 315, 675

Offset: 1

Alford Arnold, Aug 18 2007

			Row 12 of A131886 is 2048 96 72 60 so here row 12 is 177147 1215 315 675.

Cf. A001055, A025487, A050322, A057567, A077569, A108464, A122819, A130839, A131802, A131886.

cp's OEIS Frontend

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)).

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