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A188951
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Number of perfect powers (A001597) < 2^n.
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2
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0, 1, 1, 2, 4, 7, 10, 15, 22, 30, 41, 57, 81, 113, 155, 216, 298, 416, 582, 813, 1135, 1588, 2223, 3115, 4368, 6135, 8622, 12127, 17063, 24022, 33838, 47688, 67226, 94804, 133737, 188709, 266350, 376018, 530940, 749819, 1059096, 1496143, 2113801, 2986769
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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For n=3, the perfect powers smaller than 2^3=8 are: 1 and 4. So a(3) = 2.
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MATHEMATICA
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Join[{0, 1}, Table[-Sum[MoebiusMu[x]*Floor[2^(n/x) - 1], {x, 2, n}], {n, 2, 50}]]
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PROG
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(PARI) a(n) = sum(k=1, 2^n-1, (k==1) || ispower(k)); \\ Michel Marcus, Apr 11 2016
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CROSSREFS
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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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