%I A025528
%S A025528 0,1,2,3,4,4,5,6,7,7,8,8,9,9,9,10,11,11,12,12,12,12,13,13,14,14,15,15,
%T A025528 16,16,17,18,18,18,18,18,19,19,19,19,20,20,21,21,21,21,22,22,23,23,23,
%U A025528 23,24,24,24,24,24,24,25,25,26,26,26,27,27,27,28,28,28,28,29,29,30,30
%N A025528 Number of prime powers <= n with exponents >0.
%C A025528 a(n) = sum of the exponents in the prime factorization of lcm{1,2,...,
               n}.
%C A025528 Larger than but analogous to Pi(n).
%C A025528 Counts A000961 without 1=prime^0: a(n)=A065515(n)-1. - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Jul 03 2003
%D A025528 G. Tenenbaum, Introduction a la theorie analytique et probabiliste des 
               nombres, p. 203, Publications de l'Institut Cartan,1990.
%H A025528 Daniel Forgues, <a href="b025528.txt">Table of n, a(n) for n=1,...,100000</
               a>.
%H A025528 <a href="Sindx_Lc.html#lcm">Index entries for sequences related to lcm's</
               a>
%F A025528 a(n)=Cardinality[{1, .., n}|A001221(i)=1]
%F A025528 a(n)=sum(p primes <=n, floor(Log(n)/log(p))) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Apr 30 2002
%F A025528 a(n) ~ n/log(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 30 2003
%F A025528 a(n) = A069637(n) + A000720(n). - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), 
               Feb 24 2004 [Corrected by Franklin T. Adams-Watters, Jun 08 2008]
%F A025528 a(n) = A000720(n) + A000720([n^(1/2)]) + A000720([n^(1/3)]) + ... [From 
               Max Alekseyev (maxale(AT)gmail.com), May 11 2009]
%e A025528 Below 100 there are 25 primes and 25+10=35 prime powers.
%o A025528 (PARI) for(n=1,100,print1(sum(k=1,n,floor(log(n)/log(prime(k)))),","))
%o A025528 (PARI) a(n)=sum(i=1,n,if(omega(i)-1,0,1))
%Y A025528 Cf. A000961, A000040, A000720, A001221, A141228.
%Y A025528 Sequence in context: A080820 A116549 A107079 this_sequence A123580 A072894 
               A037915
%Y A025528 Adjacent sequences: A025525 A025526 A025527 this_sequence A025529 A025530 
               A025531
%K A025528 nonn
%O A025528 1,3
%A A025528 Clark Kimberling (ck6(AT)evansville.edu)
%E A025528 New description from Labos E. (labos(AT)ana.sote.hu), Nov 09 2000