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A120944 Composite squarefree numbers. 109
6, 10, 14, 15, 21, 22, 26, 30, 33, 34, 35, 38, 39, 42, 46, 51, 55, 57, 58, 62, 65, 66, 69, 70, 74, 77, 78, 82, 85, 86, 87, 91, 93, 94, 95, 102, 105, 106, 110, 111, 114, 115, 118, 119, 122, 123, 129, 130, 133, 134, 138, 141, 142, 143, 145, 146, 154, 155, 158, 159, 161 (list; graph; refs; listen; history; text; internal format)
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
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)
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
CROSSREFS
Cf. A000469 (Nonprime squarefree numbers).
Set of powers: A182853.
Sequence in context: A344585 A080365 A000469 * A327829 A052053 A276818
KEYWORD
nonn
AUTHOR
Zak Seidov, Aug 19 2006
STATUS
approved

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Last modified February 28 05:20 EST 2024. Contains 370379 sequences. (Running on oeis4.)