OFFSET
1,2
COMMENTS
These numbers are called "oddly squarefree" in Banks and Luca. - Michel Marcus, Mar 14 2016
The asymptotic density of this sequence is 8/Pi^2 (A217739). - Amiram Eldar, Sep 21 2020
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
William D. Banks and Florian Luca, Roughly squarefree values of the Euler and Carmichael functions, Acta Arithmetica, Vol. 120, No. 3 (2005), pp. 211-230.
FORMULA
MATHEMATICA
Select[Range@ 85, SquareFreeQ[#/2^IntegerExponent[#, 2]] &] (* Michael De Vlieger, Mar 15 2020 *)
PROG
(Haskell)
a122132 n = a122132_list !! (n-1)
a122132_list = filter ((== 1) . a008966 . a000265) [1..]
-- Reinhard Zumkeller, Jan 24 2012
(PARI) is(n)=issquarefree(n>>valuation(n, 2)); \\ Charles R Greathouse IV, Sep 02 2015
(Python)
from math import isqrt
from sympy import mobius
def A122132(n):
def f(x): return int(n+x-sum(mobius(k)*((x>>j)//k**2+1>>1) for j in range(x.bit_length()) for k in range(1, isqrt(x>>j)+1, 2)))
m, k = n, f(n)
while m != k: m, k = k, f(k)
return m # Chai Wah Wu, Dec 01 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Aug 21 2006
STATUS
approved