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A283050 Integers that are divisible by the square of their least prime factor.

%I A283050 #24 Mar 03 2017 04:22:57
%S A283050 4,8,9,12,16,20,24,25,27,28,32,36,40,44,45,48,49,52,56,60,63,64,68,72,
%T A283050 76,80,81,84,88,92,96,99,100,104,108,112,116,117,120,121,124,125,128,
%U A283050 132,135,136,140,144,148,152,153,156,160,164,168,169,171,172,175,176,180
%N A283050 Integers that are divisible by the square of their least prime factor.
%C A283050 Integers > 1 such that A126773(n) = 1.
%C A283050 Conjecture: 1 <= a(n+1) - a(n) <= 4. - _R. J. Cano_, Feb 27 2017
%C A283050 The conjecture is true since all multiples of 4 are in this sequence. - _Charles R Greathouse IV_, Feb 28 2017
%H A283050 Charles R Greathouse IV, <a href="/A283050/b283050.txt">Table of n, a(n) for n = 1..10000</a>
%F A283050 a(n) ~ kn where 1/k = 1/2^2 + 1/2*1/3^2 + 1/2*2/3*1/5^2 + 1/2*2/3*4/5*1/7^2 + ... = A283071 so k = 3.02940306.... - _Charles R Greathouse IV_, Feb 27 2017
%p A283050 A283050 := proc(n)
%p A283050     option remember;
%p A283050     if n =1 then
%p A283050         4 ;
%p A283050     else
%p A283050         for a from procname(n-1)+1 do
%p A283050             if A126773(a)=  1 then
%p A283050                 return a;
%p A283050             end if;
%p A283050         end do:
%p A283050     end if;
%p A283050 end proc:
%p A283050 seq(A283050(n),n=1..100) ; # _R. J. Mathar_, Mar 03 2017
%t A283050 Select[Range[2, 180], Divisible[#, FactorInteger[#][[1, 1]]^2] &] (* _Michael De Vlieger_, Feb 27 2017 *)
%o A283050 (PARI) isok(n) = !(n % factor(n)[1,1]^2);
%Y A283050 Subsequence of A013929 (numbers that are not squarefree).
%Y A283050 Cf. A126773, A283071.
%K A283050 nonn
%O A283050 1,1
%A A283050 _Michel Marcus_, Feb 27 2017