|
| |
|
|
A120944
|
|
Composite squarefree numbers.
|
|
68
|
|
|
|
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
|
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
|
| |
|
|
