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A038109 Divisible exactly by the square of a prime.

%I A038109 #24 Aug 12 2020 21:10:05
%S A038109 4,9,12,18,20,25,28,36,44,45,49,50,52,60,63,68,72,75,76,84,90,92,98,
%T A038109 99,100,108,116,117,121,124,126,132,140,144,147,148,150,153,156,164,
%U A038109 169,171,172,175,180,188,196,198,200,204,207,212,220,225,228,234,236,242
%N A038109 Divisible exactly by the square of a prime.
%C A038109 Numbers for which at least one prime factor exponent is exactly 2.
%C A038109 Sometimes called squarefull numbers, although that term is usually reserved for A001694. - _N. J. A. Sloane_, Jul 22 2012
%C A038109 The asymptotic density of this sequence is 1 - A330596 = 0.2514647... - _Amiram Eldar_, Aug 12 2020
%H A038109 R. J. Mathar, <a href="/A038109/b038109.txt">Table of n, a(n) for n = 1..1247</a>
%e A038109 20=5*2*2 is divisible by 2^2.
%p A038109 isA038109 := proc(n)
%p A038109     local p;
%p A038109     for p in ifactors(n)[2] do
%p A038109         if op(2,p) = 2 then
%p A038109             return true;
%p A038109         end if;
%p A038109     end do:
%p A038109     false ;
%p A038109 end proc: # _R. J. Mathar_, Dec 08 2015
%p A038109 # second Maple program:
%p A038109 q:= n-> ormap(i-> i[2]=2, ifactors(n)[2]):
%p A038109 select(q, [$1..300])[];  # _Alois P. Heinz_, Aug 12 2020
%t A038109 Select[Range[250],MemberQ[Transpose[FactorInteger[#]][[2]],2]&] (* _Harvey P. Dale_, Sep 24 2012 *)
%o A038109 (PARI) is(n)=#select(n->n==2, Set(factor(n)[,2])) \\ _Charles R Greathouse IV_, Sep 17 2015
%Y A038109 Cf. A001694, A013929, A284017, A284018.
%K A038109 nonn,easy
%O A038109 1,1
%A A038109 _Felice Russo_
%E A038109 Corrected and extended by _Erich Friedman_