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Search: id:A069623
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| A069623 |
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Number of perfect powers <= n. |
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+0
5
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| 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
(list; graph; listen)
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OFFSET
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1,4
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LINKS
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Eric Weisstein's World of Mathematics, Perfect Powers.
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FORMULA
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a(n) = n - Sum_{k = 1 to [log2(n)]} mu(k)*[n^(1/k)-1]), where mu = A008683. - David W. Wilson, Oct 09, 2002
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EXAMPLE
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a(27) = 7 as the perfect powers <= 27 are 1, 4, 8, 9, 16, 25 and 27.
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MATHEMATICA
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a[1] = 1; a[n_] := If[ !PrimeQ[n] && GCD @@ Last[Transpose[FactorInteger[n]]] > 1, a[n - 1] + 1, a[n - 1]]; Table[a[n], {n, 1, 85}]
(* Or *) b[n_] := n - Sum[ MoebiusMu[k] * Floor[n^(1/k) - 1], {k, 1, Floor[ Log[2, n]]}]; Table[b[n], {n, 1, 85}]
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CROSSREFS
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Perfect powers are A001597. Cf. A053289. A076411 is another version.
Sequence in context: A071136 A025425 A085501 this_sequence A076411 A072613 A029551
Adjacent sequences: A069620 A069621 A069622 this_sequence A069624 A069625 A069626
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 27 2002
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