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A000469
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1 together with products of 2 or more distinct primes.
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42
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1, 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
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OFFSET
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1,2
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COMMENTS
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Nonprime squarefree numbers.
Except for 1, composite n such that the squarefree part of n is greater than phi(n). - Benoit Cloitre, Apr 06 2002
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
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FORMULA
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n such that A007913(n)>A000010(n). - Benoit Cloitre, Apr 06 2002
N-floor(N/p1) - floor(N/(p2) - ... - floor(N/p(i) + floor(N/(c2) + floor(N/(c3)+ ... + floor(N/c(j)-1 where N is any number; p1,p2 are the primes with p(i) being the first prime > square root of N and c2, c3 are the numbers other than 1 in this sequence with c(j) <= N will yield the number of primes less than or equal to N other than p1, p2, ..., p(i). - Ben Paul Thurston, Aug 15 2007
A005171(a(n))*A008966(a(n)) = 1. - Reinhard Zumkeller, Nov 01 2009
Sum(n=1, Infinity, 1/a(n)^s) = Zeta(s)/Zeta(2s) - PrimeZeta(s). - Enrique Pérez Herrero, Mar 31 2012
n such that A001221(n) = A001222(n), n nonprime. - Carlos Eduardo Olivieri, Aug 06 2015
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MAPLE
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select(numtheory:-issqrfree and not isprime, [$1..1000]); # Robert Israel, Aug 06 2015
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MATHEMATICA
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lst={}; Do[If[SquareFreeQ[n], If[ !PrimeQ[n], AppendTo[lst, n]]], {n, 200}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 20 2009 *)
With[{upto=200}, Complement[Select[Range[upto], SquareFreeQ], Prime[ Range[ PrimePi[ upto]]]]] (* Harvey P. Dale, Oct 01 2011 *)
Select[Range[200], !PrimeQ[#] && PrimeOmega[#] == PrimeNu[#] &] (* Carlos Eduardo Olivieri, Aug 06 2015 *)
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PROG
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(PARI) for(n=0, 64, if(isprime(n), n+1, if(issquarefree(n), print(n))))
(PARI) for(n=1, 160, if(core(n)*(1-isprime(n))>eulerphi(n), print1(n, ", ")))
(Haskell)
a000469 n = a000469_list !! (n-1)
a000469_list = filter ((== 0) . a010051) a005117_list
-- Reinhard Zumkeller, Mar 21 2014
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CROSSREFS
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Cf. A005117, A007913, A000010, A010051, A239508, A239509, A120944 (composite squarefree numbers, same sequence apart from the first term).
Sequence in context: A212168 A344585 A080365 * A120944 A327829 A052053
Adjacent sequences: A000466 A000467 A000468 * A000470 A000471 A000472
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Dan Bentley (dtb(AT)research.att.com)
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STATUS
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approved
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