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A072750 Counting factor 7 in the first n squarefree numbers. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

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

LINKS

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

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 A186437 A029835

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

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Last modified March 28 17:42 EDT 2020. Contains 333095 sequences. (Running on oeis4.)