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