A120944 Composite squarefree numbers.

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

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)

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).

Cf. A001221, A001222, A002808, A005117, A008966, A010051.

Set of powers: A182853.

Sequence in context: A344585 A080365 A000469 * A327829 A052053 A276818

Adjacent sequences: A120941 A120942 A120943 * A120945 A120946 A120947

Keyword

nonn

Author

Zak Seidov, Aug 19 2006

Status

approved