A072748 Counting factor 3 in the first n squarefree numbers.

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, 10, 10, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 17, 17, 17, 17, 17, 18, 18, 19, 19, 19, 19, 19, 20, 20, 21, 21

Offset: 1

Author

Reinhard Zumkeller, Jul 08 2002

Keywords

• nonn

Examples

			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.
		

Links

• Gheorghe Coserea, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A072747, A072749, A072750, A072751.

Programs

Mathematica

Accumulate[If[Divisible[#, 3], 1, 0]&/@Select[Range[100], SquareFreeQ]] (* Vincenzo Librandi, Aug 23 2015 *)

PARI

n = 80; k = 0; bag = List(); a = vector(n);
until(n == 0, k++; if (issquarefree(k), listput(bag, k); n--));
for (i=2, #bag, a[i] = a[i-1] + (bag[i] % 3 == 0));
print(a); \\ Gheorghe Coserea, Aug 22 2015

Formula

a(n) ~ n/4. - Amiram Eldar, Feb 24 2021

Extensions

Name clarified by Gheorghe Coserea, Aug 22 2015