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Count of factors of 5 in the first n squarefree numbers.
5

%I #20 Feb 24 2021 03:50:55

%S 0,0,0,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,

%T 6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,

%U 11,11,11,12,12,12,12,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14

%N Count of factors of 5 in the first n squarefree numbers.

%H Gheorghe Coserea, <a href="/A072749/b072749.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ n/6. - _Amiram Eldar_, Feb 24 2021

%e The first 10 squarefree numbers are: 1, 2, 3, 5, 6=2*3, 7, 10=2*5, 11, 13 and 14=2*7: 5 and 10 are divisible by 5, therefore a(10)=2.

%t Accumulate[If[Divisible[#,5],1,0]&/@Select[Range[150],SquareFreeQ]] (* _Harvey P. Dale_, Oct 17 2013 *)

%o (PARI)

%o n = 89; k = 0; bag = List(); a = vector(n);

%o until(n == 0, k++; if (issquarefree(k), listput(bag, k); n--));

%o for (i=2, #bag, a[i] = a[i-1] + (bag[i] % 5 == 0));

%o print(a); \\ _Gheorghe Coserea_, Aug 22 2015

%Y Cf. A005117, A072747, A072748, A072750, A072751.

%K nonn

%O 1,7

%A _Reinhard Zumkeller_, Jul 08 2002

%E Name clarified by _Gheorghe Coserea_, Aug 22 2015