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A070228 Number of perfect powers (A001597) not exceeding 2^n. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = 1 - Sum_{x=2..n} Moebius(n)*floor(2^(n/x)-1). - Robert G. Wilson v, Jan 20 2015

EXAMPLE

How many powers are there not exceeding 2^4?: 1 4 8 9 16 =(5). a(22)=2224: there are 2224 powers not exceeding 2^22.

MATHEMATICA

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 *)

PROG

(PARI) for(x=0, 62, print(x, " ", sum(1, n=2, x, -mu(n)*floor(2^(x/n)-1)) ) )

CROSSREFS

Cf. A070428.

Sequence in context: A320593 A006336 A175831 * A173599 A006304 A238591

Adjacent sequences:  A070225 A070226 A070227 * A070229 A070230 A070231

KEYWORD

nonn,easy

AUTHOR

Donald S. McDonald, May 14 2002

EXTENSIONS

a(39)-a(44) from Alex Ratushnyak, Jan 02 2014

STATUS

approved

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Last modified August 23 13:45 EDT 2019. Contains 326227 sequences. (Running on oeis4.)