%I A144338
%S A144338 2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,26,29,30,31,33,34,35,37,38,39,
%T A144338 41,42,43,46,47,51,53,55,57,58,59,61,62,65,66,67,69,70,71,73,74,77,78,
               79,
%U A144338 82,83,85,86,87,89,91,93,94,95,97,101,102,103,105,106,107,109,110,111,
               113
%N A144338 Square-free numbers > 1.
%C A144338 Nontrivial products of distinct primes. Sequence A005117 without the 
               initial 1.
%C A144338 Also numbers n for which the following equation holds : (2^r)-sigma_0(p(1)*...*p(r)) 
               = 0. This sequence describes the way RMS numbers (A140480) are grouped. 
               In general if n = p(1)^alfa(1) *...* p(s)^alfa(s), alfa(i)>=1, we 
               have the equation [2^sum_i=1..s{alfa(i)}] - sigma_0(p(1)^alfa(1) 
               *...* p(s)^alfa(s)) = T. In terms of OEIS sequences the equation 
               is : 2^(A001055(n)) - (A000005(n)) = T. This sequence has T=0, n=p(1)*...*p(r). 
               If T=(2^k)-(k+1) then n=p^k. T splits the set of integers into subsets 
               according to the form of prime factorization of the number n.
%C A144338 These can be computed with a modified Sieve of Eratosthenes: [1] start 
               at n=2, [2] if (n is crossed out an even number of times) then (append 
               n to the sequence and cross out all multiples of n), [3] set n:=n+1 
               and go to step 2; compare with the sieve for the complement of perfect 
               powers in A007916. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 19 2009]
%H A144338 S. R. Finch, <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.9320">
               Kalmar's Composition Constant</a>, CiteSeer (2003).
%H A144338 Eric Weisstein's World of Math, <a href="http://mathworld.wolfram.com/
               OrderedFactorization.html">Ordered Factorization</a>
%H A144338 <a href="Sindx_Si.html#sieve">Index entries for sequences generated by 
               sieves</a> [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 19 2009]
%Y A144338 Cf. A001055, A140480, A000005
%Y A144338 Sequence in context: A064594 A076144 A005117 this_sequence A077377 A076786 
               A167171
%Y A144338 Adjacent sequences: A144335 A144336 A144337 this_sequence A144339 A144340 
               A144341
%K A144338 easy,nonn
%O A144338 1,1
%A A144338 Ctibor O. Zizka (c.zizka(AT)email.cz), Sep 18 2008
%E A144338 Corrected A-number typo R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Feb 21 2009