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A072292
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Number of proper powers b^d <= n (b > 1, d > 1).
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2
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0, 0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 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, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11
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OFFSET
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1,8
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COMMENTS
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Base b = 1 is excluded since 1 would be 1^d for any degree d (degree of power not well defined).
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LINKS
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MATHEMATICA
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a[n_] := (pp = Reap[ Do[ If[b^d <= n, Sow[b^d]], {b, 2, Sqrt[n]}, {d, 2, Log[2, n]}]]; If[pp == {Null, {}}, 0, Length[ Union[ pp[[2, 1]]]]]); Table[a[n], {n, 1, 90}](* Jean-François Alcover, May 16 2012 *)
Module[{nn=10, pp}, pp=Union[Flatten[Table[a^b, {a, 2, nn}, {b, 2, nn}]]]; Accumulate[ Table[ If[ MemberQ[pp, n], 1, 0], {n, 2^nn}]]] (* Harvey P. Dale, Nov 14 2022 *)
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PROG
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(PARI) A072292(n)=n=floor(n)+.5; -sum(k=2, log(n)\log(2), floor(n^(1/k)-1)*moebius(k))
(Haskell)
a072292 n = a072292_list !! (n-1)
a072292_list = scanl (+) 0 $ tail a075802_list
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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