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A061398
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Number of squarefree integers between prime(n) and prime(n+1).
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7
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0, 0, 1, 1, 0, 2, 0, 2, 1, 1, 3, 2, 1, 1, 1, 3, 0, 3, 2, 0, 3, 1, 3, 4, 0, 1, 2, 0, 2, 6, 2, 2, 1, 5, 0, 2, 3, 2, 1, 3, 0, 6, 0, 2, 0, 7, 8, 1, 0, 2, 3, 0, 3, 3, 3, 3, 0, 2, 1, 1, 5, 7, 2, 0, 1, 9, 2, 4, 0, 0, 4, 3, 2, 2, 2, 2, 5, 2, 4, 6, 0, 5, 0, 4, 1, 3, 4, 1, 1, 2, 6, 4, 1, 4, 2, 2, 7, 0, 8, 4, 4, 3, 2, 1, 2
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OFFSET
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1,6
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 1..1000
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FORMULA
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a(n) = A013928(A000040(n+1)) - A013928(A000040(n)) - 1. - Robert Israel, Jan 06 2017
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EXAMPLE
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Between 113 and 127 the 6 squarefree numbers are 114, 115, 118, 119, 122, 123, so a(30)=6.
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MAPLE
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p:= 2:
for n from 1 to 200 do
q:= nextprime(p);
A[n]:= nops(select(numtheory:-issqrfree, [$p+1..q-1]));
p:= q;
od:
seq(A[i], i=1..200); # Robert Israel, Jan 06 2017
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MATHEMATICA
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a[n_] := Count[Range[Prime[n]+1, Prime[n+1]-1], _?SquareFreeQ];
Array[a, 100] (* Jean-François Alcover, Feb 28 2019 *)
Count[Range[#[[1]]+1, #[[2]]-1], _?(SquareFreeQ[#]&)]&/@Partition[ Prime[ Range[120]], 2, 1] (* Harvey P. Dale, Oct 14 2021 *)
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PROG
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(PARI) { n=0; q=2; forprime (p=3, prime(1001), a=0; for (i=q+1, p-1, a+=issquarefree(i)); write("b061398.txt", n++, " ", a); q=p ) } \\ Harry J. Smith, Jul 22 2009
(PARI) a(n) = my(pp=prime(n)+1); sum(k=pp, nextprime(pp)-1, issquarefree(k)); \\ Michel Marcus, Feb 28 2019
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CROSSREFS
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Cf. A000040, A005117, A013928.
Cf. A179211. [Reinhard Zumkeller, Jul 05 2010]
Sequence in context: A055651 A175929 A079627 * A080232 A008482 A037012
Adjacent sequences: A061395 A061396 A061397 * A061399 A061400 A061401
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Jun 07 2001
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STATUS
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approved
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