Dear Math Fun, Does anyone know the asymptotics for this sequence? (I did a crude estimate, but I have no confidence in it.) Thanks! Neil %I A070548 %S A070548 1,1,1,1,1,2,2,2,2,3,3,3,3,4,5,5,5,5,5,5,6,7,7,7,7,8,8,8,8,8,8,8,9,10, %T A070548 11,11,11,12,13,13,13,13,13,13,13,14,14,14,14,14,15,15,15,15,16,16,17, %U A070548 18,18,18,18,19,19,19,20,20,20,20,21,21,21,21,21,22,22,22,23,23,23,23 %N A070548 a(n) = Card{ k in range 1<=k<=n such that Moebius(k)=1 }. %C A070548 Moebius(k)=1 iff k is the product of an even number of distinct primes (cf. A008683). See A057627 for Moebius(k)=0. %H A070548 N. J. A. Sloane, <a href="http://www.research.att.com/~njas/sequences/b070548.txt">Table of n, a(n) for n = 1..10000</a> %o A070548 (PARI) for(n=1,150,print1(sum(i=1,n,if(moebius(i)-1,0,1)),",")) %Y A070548 Cf. A008683. Equals A072613(n) + 1. %K A070548 easy,nonn %O A070548 1,6 %A A070548 Benoit Cloitre (benoit7848c(AT)orange.fr), May 02 2002