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A072748 Counting factor 3 in the first n squarefree numbers.

%I A072748 #19 Feb 24 2021 03:50:39
%S A072748 0,0,1,1,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,6,6,6,6,6,7,7,8,8,8,8,9,9,9,
%T A072748 10,10,10,10,10,10,11,11,12,12,12,12,12,12,13,13,13,13,13,13,14,14,14,
%U A072748 15,15,15,15,15,16,16,17,17,17,17,17,18,18,19,19,19,19,19,20,20,21,21
%N A072748 Counting factor 3 in the first n squarefree numbers.
%H A072748 Gheorghe Coserea, <a href="/A072748/b072748.txt">Table of n, a(n) for n = 1..10000</a>
%F A072748 a(n) ~ n/4. - _Amiram Eldar_, Feb 24 2021
%e A072748 The first 10 squarefree numbers are: 1, 2, 3, 5, 6=2*3, 7, 10=2*5, 11, 13 and 14=2*7: 3 and 6 are divisible by 3, therefore a(10)=2.
%t A072748 Accumulate[If[Divisible[#, 3], 1, 0]&/@Select[Range[100], SquareFreeQ]] (* _Vincenzo Librandi_, Aug 23 2015 *)
%o A072748 (PARI)
%o A072748 n = 80; k = 0; bag = List(); a = vector(n);
%o A072748 until(n == 0, k++; if (issquarefree(k), listput(bag, k); n--));
%o A072748 for (i=2, #bag, a[i] = a[i-1] + (bag[i] % 3 == 0));
%o A072748 print(a); \\ _Gheorghe Coserea_, Aug 22 2015
%Y A072748 Cf. A005117, A072747, A072749, A072750, A072751.
%K A072748 nonn
%O A072748 1,5
%A A072748 _Reinhard Zumkeller_, Jul 08 2002
%E A072748 Name clarified by _Gheorghe Coserea_, Aug 22 2015