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A072747 Counting factor 2 in the first n squarefree numbers.

%I A072747 #20 Feb 24 2021 03:50:17
%S A072747 0,1,1,1,2,2,3,3,3,4,4,4,4,4,5,5,6,6,7,7,7,8,8,8,9,9,9,10,10,11,11,11,
%T A072747 11,11,11,12,12,12,13,13,14,14,14,15,15,15,16,16,17,17,18,18,18,19,19,
%U A072747 19,19,19,20,20,20,20,21,21,21,22,22,22,23,23,23,24,24,25,25,26,26,26
%N A072747 Counting factor 2 in the first n squarefree numbers.
%H A072747 Gheorghe Coserea, <a href="/A072747/b072747.txt">Table of n, a(n) for n = 1..10000</a>
%F A072747 a(n) ~ n/3. - _Amiram Eldar_, Feb 24 2021
%e A072747 The first 10 squarefree numbers are: 1, 2, 3, 5, 6=2*3, 7, 10=2*5, 11, 13 and 14=2*7: 2, 6, 10 and 14 are divisible by 2, therefore a(10)=4.
%t A072747 Accumulate[If[Divisible[#, 2], 1, 0]&/@Select[Range[100], SquareFreeQ]] (* _Vincenzo Librandi_, Aug 23 2015 *)
%o A072747 (PARI)
%o A072747 n = 77; k = 0; bag = List(); a = vector(n);
%o A072747 until(n == 0, k++; if (issquarefree(k), listput(bag, k); n--));
%o A072747 for (i=2, #bag, a[i] = a[i-1] + (bag[i] % 2 == 0)); print(a); \\ _Gheorghe Coserea_, Aug 22 2015
%Y A072747 Cf. A005117, A072748, A072749, A072750, A072751.
%K A072747 nonn
%O A072747 1,5
%A A072747 _Reinhard Zumkeller_, Jul 08 2002
%E A072747 Name clarified by _Gheorghe Coserea_, Aug 22 2015