OFFSET
1,1
COMMENTS
Intersection of A002808 and A005117: n > 1 such that A008966(n) * (1-A010051(n)) = 1. - Reinhard Zumkeller, Dec 19 2011
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
From Enrique Pérez Herrero, Apr 01 2012: (Start)
Solutions to floor(omega(x)/bigomega(x))*(1-floor(1/bigomega(x))) = 1, where bigomega is A001222 and omega is A001221.
Sum_{n>=1} 1/a(n)^s = zeta(s)/zeta(2s) - 1 - PrimeZeta(s). (End)
a(n) = kn + O(n/log n) where k = Pi^2/6. - Charles R Greathouse IV, Aug 02 2024
MAPLE
select(not(isprime) and numtheory:-issqrfree, [$2..1000]); # Robert Israel, Jul 07 2015
MATHEMATICA
lst={}; Do[If[SquareFreeQ[n], If[ !PrimeQ[n], AppendTo[lst, n]]], {n, 2, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 20 2009; updated by Jean-François Alcover, Jun 19 2013 *)
Select[Range[200], PrimeNu[#] > 1 && SquareFreeQ[#] &] (* Carlos Eduardo Olivieri, Jul 07 2015 *)
PROG
(Magma) [n: n in [6..161] | IsSquarefree(n) and not IsPrime(n)]; // Bruno Berselli, Mar 03 2011
(Haskell)
a120944 n = a120944_list !! (n-1)
a120944_list = filter ((== 1) . a008966) a002808_list
-- Reinhard Zumkeller, Dec 19 2011
(PARI) is(n)=issquarefree(n)&&!isprime(n)&&n>1 \\ Charles R Greathouse IV, Apr 11 2012
(Python)
from sympy import factorint
def ok(n): f = factorint(n); return len(f) > 1 and all(f[p] < 2 for p in f)
print(list(filter(ok, range(1, 162)))) # Michael S. Branicky, Jun 10 2021
(Python)
from math import isqrt
from sympy import primepi, mobius
def A120944(n):
def f(x): return n+1+primepi(x)+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
m, k = n+1, f(n+1)
while m != k:
m, k = k, f(k)
return m # Chai Wah Wu, Aug 02 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Aug 19 2006
STATUS
approved