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A070228 Number of perfect powers (A001597) not exceeding 2^n. 2

%I

%S 1,1,2,3,5,8,11,16,23,31,42,58,82,114,156,217,299,417,583,814,1136,

%T 1589,2224,3116,4369,6136,8623,12128,17064,24023,33839,47689,67227,

%U 94805,133738,188710,266351,376019,530941,749820,1059097,1496144,2113802,2986770,4220666

%N Number of perfect powers (A001597) not exceeding 2^n.

%H Robert G. Wilson v, <a href="/A070228/b070228.txt">Table of n, a(n) for n = 0..1000</a>

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

%e 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.

%t 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 *)

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

%Y Cf. A070428.

%K nonn,easy

%O 0,3

%A _Donald S. McDonald_, May 14 2002

%E a(39)-a(44) from _Alex Ratushnyak_, Jan 02 2014

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)