A072747 Counting factor 2 in the first n squarefree numbers.

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, 11, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 25, 25, 26, 26, 26

Offset

1,5

Links

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

Formula

a(n) ~ n/3. - Amiram Eldar, Feb 24 2021

Example

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.

Mathematica

Accumulate[If[Divisible[#, 2], 1, 0]&/@Select[Range[100], SquareFreeQ]] (* Vincenzo Librandi, Aug 23 2015 *)

Prog

(PARI)
n = 77; 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] % 2 == 0)); print(a); \\ Gheorghe Coserea, Aug 22 2015

Crossrefs

Cf. A005117, A072748, A072749, A072750, A072751.

Sequence in context: A259899 A365275 A071996 * A194295 A194287 A194303

Adjacent sequences: A072744 A072745 A072746 * A072748 A072749 A072750

Keyword

nonn

Author

Reinhard Zumkeller, Jul 08 2002

Extensions

Name clarified by Gheorghe Coserea, Aug 22 2015

Status

approved