A181800 - OEIS

A181800

Powerful numbers that are the least integer of their prime signature.

1, 4, 8, 16, 32, 36, 64, 72, 128, 144, 216, 256, 288, 432, 512, 576, 864, 900, 1024, 1152, 1296, 1728, 1800, 2048, 2304, 2592, 3456, 3600, 4096, 4608, 5184, 5400, 6912, 7200, 7776, 8192, 9216, 10368, 10800, 13824, 14400, 15552, 16384, 18432, 20736, 21600, 27000

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OFFSET

1,2

COMMENTS

Apart from 1, all terms in this sequence are multiples of 4. - Charles R Greathouse IV, Dec 13 2016

Apart from 1, the prime factor exponents of the terms in this sequence represent exactly every factorization of every integer k >= 2. E.g. the two factorizations of 4 are represented by 16 (2^4 -> {4}) and 36 (2^2 * 3^2 -> {2, 2}; 2 * 2 = 4). The smallest such term for each k is subsequence A085629. - Charles L. Hohn, Apr 04 2025

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Charles R Greathouse IV)

FORMULA

Intersection of A001694 and A025487.

PROG

(PARI) is(n)=if(n<4, return(n==1)); my(f=factor(n)); vecmin(f[, 2])>1 && f[, 1]~ == primes(#f~) && f[, 2] == vecsort(f[, 2], , 4) \\ Charles R Greathouse IV, Sep 14 2015

CROSSREFS

Cf. A001694 (powerful numbers), A025487 (least integer of each prime signature).

Cf. A085629.

Sequence in context: A391627 A390010 A387901 * A319180 A075090 A354955

Adjacent sequences: A181797 A181798 A181799 * A181801 A181802 A181803

KEYWORD

nonn

AUTHOR

Matthew Vandermast, Dec 02 2010

STATUS

approved