A072749 Count of factors of 5 in the first n squarefree numbers.

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, 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, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14

Offset

1,7

Links

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

Formula

a(n) ~ n/6. - 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: 5 and 10 are divisible by 5, therefore a(10)=2.

Mathematica

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

Prog

(PARI)
n = 89; 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] % 5 == 0));
print(a); \\ Gheorghe Coserea, Aug 22 2015

Crossrefs

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

Sequence in context: A000523 A124156 A324965 * A066490 A156685 A124230

Adjacent sequences: A072746 A072747 A072748 * A072750 A072751 A072752

Keyword

nonn

Author

Reinhard Zumkeller, Jul 08 2002

Extensions

Name clarified by Gheorghe Coserea, Aug 22 2015

Status

approved