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A076411
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Number of perfect powers < n.
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4
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0, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12
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OFFSET
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1,5
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COMMENTS
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Perfect powers are in A001597. The function a(n) increases much more slowly than pi(n): e.g., a(1765)=54 and pi(1765)=274. See also A076412.
This is essentially the same as A069623 which is the main entry, see there for more formulas. - M. F. Hasler, Aug 16 2015
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LINKS
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FORMULA
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a(n) = n^(1/2) + n^(1/3) + n^(1/5) - n^(1/6) + n^(1/7) - n^(1/10) + O(n^(1/11)). - Charles R Greathouse IV, Aug 14 2015
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EXAMPLE
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a(9)=3 because there are 3 perfect powers less than 9: 1,4,8.
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MATHEMATICA
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Join[{0}, Accumulate[Table[If[GCD@@FactorInteger[n][[All, 2]]>1, 1, 0], {n, 90}]]+1] (* Harvey P. Dale, Mar 19 2020 *)
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PROG
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CROSSREFS
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A069623(n) = a(n+1) is the main entry.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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