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A070228
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Number of perfect powers (A001597) not exceeding 2^n.
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3
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1, 1, 2, 3, 5, 8, 11, 16, 23, 31, 42, 58, 82, 114, 156, 217, 299, 417, 583, 814, 1136, 1589, 2224, 3116, 4369, 6136, 8623, 12128, 17064, 24023, 33839, 47689, 67227, 94805, 133738, 188710, 266351, 376019, 530941, 749820, 1059097, 1496144, 2113802, 2986770, 4220666
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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How many powers are there not exceeding 2^4?: 1, 4, 8, 9, 16. Hence a(4) = 5.
a(22)=2224: there are 2224 powers not exceeding 2^22.
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MATHEMATICA
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f[n_] := 1 - Sum[ MoebiusMu[x]*Floor[2^(n/x) - 1], {x, 2, n}]; Array[f, 44, 0] (* Robert G. Wilson v, Jan 20 2015 *)
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PROG
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(PARI) a(n) = 1 - sum(k=2, n, moebius(k)*(sqrtnint(2^n, k)-1));
(Python)
from sympy import mobius, integer_nthroot
def A070228(n): return int(1+sum(mobius(x)*(1-integer_nthroot(1<<n, x)[0]) for x in range(2, n+1))) # Chai Wah Wu, Aug 13 2024
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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