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A057627
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Number of nonsquarefree numbers not exceeding n.
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23
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0, 0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 9, 9, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 16, 16, 16, 17, 18, 19, 19, 20, 20, 21, 21, 22, 22, 22, 22, 23, 23, 23, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 28, 29, 29, 29
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OFFSET
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1,8
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COMMENTS
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Number of integers k in A013929 in the range 1 <= k <= n.
This sequence is different from A013940, albeit the first 35 terms are identical.
Number of partitions of 2n into two parts with the smallest part nonsquarefree. - Wesley Ivan Hurt, Oct 25 2017
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LINKS
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FORMULA
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a(n) = n - A013928(n+1) = n - Sum_{k=1..n} mu(k)^2.
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EXAMPLE
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a(36)=13 because 13 nonsquarefree numbers exist which do not exceed 36:{4,8,9,12,16,18,20,24,25,27,28,32,36}.
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MAPLE
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N:= 1000: # to get terms up to a(N)
B:= Array(1..N, numtheory:-issqrfree):
C:= map(`if`, B, 0, 1):
A:= map(round, Statistics:-CumulativeSum(C)):
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MATHEMATICA
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Accumulate[Table[If[SquareFreeQ[n], 0, 1], {n, 80}]] (* Harvey P. Dale, Jun 04 2014 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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