A072750 Counting factor 7 in the first n squarefree numbers.

0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12

Offset

1,10

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) - a(n-1) = 1 if A005117(n) is in A008589, otherwise 0. - Robert Israel, Aug 23 2015

a(n) ~ n/8. - 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: 7 and 14 are divisible by 7, therefore a(10)=2.

Maple

N:= 1000: # to use the squarefree numbers <= N
M:= map(proc(t) if numtheory:-issqrfree(t) then if t mod 7 = 0 then 1 else 0 fi fi end proc, [$1..N]):
ListTools:-PartialSums(M); # Robert Israel, Aug 23 2015

Mathematica

With[{sf=Select[Range[200], SquareFreeQ]}, Accumulate[If[Divisible[#, 7], 1, 0]&/@sf]] (* Harvey P. Dale, Mar 21 2013 *)

Prog

(Haskell)
a072750 n = a072750_list !! (n-1)
a072750_list = scanl1 (+) $ map ((0 ^) . (`mod` 7)) a005117_list
-- Reinhard Zumkeller, Mar 25 2013
(PARI)
n = 94; 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] % 7 == 0));
print(a); \\ Gheorghe Coserea, Aug 23 2015

Crossrefs

Cf. A005117, A008589, A072747, A072748, A072749, A072751.

Sequence in context: A309398 A171626 A074279 * A235037 A347966 A186437

Adjacent sequences: A072747 A072748 A072749 * A072751 A072752 A072753

Keyword

nonn

Author

Reinhard Zumkeller, Jul 08 2002

Extensions

Name clarified by Gheorghe Coserea, Aug 23 2015

Status

approved