

A072747


Counting factor 2 in the first n squarefree numbers.


5



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
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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[i1] + (bag[i] % 2 == 0)); print(a); \\ Gheorghe Coserea, Aug 22 2015


CROSSREFS

Cf. A005117, A072748, A072749, A072750, A072751.
Sequence in context: A034463 A259899 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



