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

1,5

Links

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

Formula

a(n) ~ n/4. - 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: 3 and 6 are divisible by 3, therefore a(10)=2.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A131996 A090618 A186444 * A174631 A278949 A030603

Adjacent sequences: A072745 A072746 A072747 * A072749 A072750 A072751

Keyword

nonn

Author

Reinhard Zumkeller, Jul 08 2002

Extensions

Name clarified by Gheorghe Coserea, Aug 22 2015

Status

approved