A304449 - OEIS

A304449

Numbers that are either squarefree or a perfect power.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

First differs from A072774 at a(105) = 144, A072774(105) = 145.

Apparently the 1 and the members of A062770. - R. J. Mathar, May 22 2018

LINKS

Table of n, a(n) for n=1..67.

FORMULA

Union of A005117 and A001597. Complement of A303946.

MATHEMATICA

Select[Range[150], SquareFreeQ[#]||GCD@@FactorInteger[#][[All, 2]]>1&]

PROG

(PARI) isok(n) = issquarefree(n) || ispower(n); \\ Michel Marcus, May 13 2018

(Python)

from math import isqrt

from sympy import mobius, integer_nthroot

def A304449(n):

def f(x): return int(n+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))+sum(mobius(k)*(integer_nthroot(x, k)[0]-1) for k in range(2, x.bit_length())))

m, k = n, f(n)

while m != k:

m, k = k, f(k)

return m # Chai Wah Wu, Aug 19 2024

CROSSREFS

Cf. A000009, A000720, A000837, A000837, A001222, A001597, A005117, A007916, A013929, A047966, A072774, A073576, A126706, A303554, A303946.

Sequence in context: A271113 A325369 A317101 * A085924 A242414 A360249

Adjacent sequences: A304446 A304447 A304448 * A304450 A304451 A304452

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 12 2018

STATUS

approved