|
%I #24 Oct 01 2023 02:39:32
%S 0,1,2,2,3,3,4,4,4,4,5,5,6,6,6,6,7,7,8,8,8,8,9,9,9,9,9,9,10,11,12,12,
%T 12,12,12,12,13,13,13,13,14,15,16,16,16,16,17,17,17,17,17,17,18,18,18,
%U 18,18,18,19,19,20,20,20,20,20,21,22,22,22,23,24,24,25,25,25,25,25,26
%N a(n) = Cardinality{ k in range 1 <= k <= n such that Moebius(k) = -1 }.
%C mu(k)=-1 if k is the product of an odd number of distinct primes. See A057627 for mu(k)=0.
%H Robert Israel, <a href="/A070549/b070549.txt">Table of n, a(n) for n = 1..10000</a>
%F From _Amiram Eldar_, Oct 01 2023: (Start)
%F a(n) = (A013928(n+1) - A002321(n))/2.
%F a(n) = A013928(n+1) - A070548(n).
%F a(n) = A070548(n) - A002321(n).
%F a(n) ~ (3/Pi^2) * n. (End)
%p ListTools:-PartialSums([seq(-min(numtheory:-mobius(n),0),n=1..100)]); # _Robert Israel_, Jan 08 2018
%t a[n_]:=Sum[Boole[MoebiusMu[k]==-1],{k,n}]; Array[a,78] (* _Stefano Spezia_, Jan 30 2023 *)
%o (PARI) for(n=1,150,print1(sum(i=1,n,if(moebius(i)+1,0,1)),","))
%Y Cf. A008683, A057627.
%Y Partial sums of A252233.
%Y Cf. A002321, A013928, A030059, A070548, A104141.
%K easy,nonn
%O 1,3
%A _Benoit Cloitre_, May 02 2002
|
