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Numbers having exactly one square divisor > 1.
10

%I #23 Dec 02 2020 18:01:48

%S 4,8,9,12,18,20,24,25,27,28,40,44,45,49,50,52,54,56,60,63,68,75,76,84,

%T 88,90,92,98,99,104,116,117,120,121,124,125,126,132,135,136,140,147,

%U 148,150,152,153,156,164,168,169,171,172,175,184,188,189,198,204,207,212

%N Numbers having exactly one square divisor > 1.

%C Numbers of the form m*p^2, p prime and m squarefree (A005117). [Corrected by _Peter Munn_, Nov 17 2020]

%C The asymptotic density of this sequence is (6/Pi^2)*Sum_{n>=1} 1/prime(n)^2 = 0.274933... (A222056). - _Amiram Eldar_, Jul 07 2020

%H Amiram Eldar, <a href="/A082293/b082293.txt">Table of n, a(n) for n = 1..10000</a>

%F A046951(a(n)) = 2.

%t Select[Range[2, 200], MemberQ[{2, 3}, (e = Sort[FactorInteger[#][[;; , 2]]])[[-1]]] && (Length[e] == 1 || e[[-2]] == 1) &] (* _Amiram Eldar_, Jul 07 2020 *)

%o (PARI) is(n)=my(f=vecsort(factor(n)[,2],,4)); #f && f[1]>1 && f[1]<4 && (#f==1 || f[2]==1) \\ _Charles R Greathouse IV_, Oct 16 2015

%Y Cf. A005117, A046951, A222056.

%Y Complement of A048111 within A013929.

%Y Subsequence of A252849.

%Y Disjoint union of A048109 and A060687.

%Y A285508 is a subsequence.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Apr 08 2003