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A136110 Limiting sequence when we start with the positive integers (A000027) and delete in step n >= 1 the term at position n + tau(a(n)), where tau(k) is the number of divisors of k.

%I A136110 #12 Mar 31 2012 14:39:55
%S A136110 1,3,4,6,7,9,12,13,15,17,18,22,23,24,28,29,30,32,33,36,37,38,43,44,47,
%T A136110 49,51,52,55,56,58,59,62,65,66,68,70,72,73,74,78,79,80,84,85,86,88,90,
%U A136110 92,94,96,97,98,104,105,106,108,109,111,116,118,119,121,122,126,129,130
%N A136110 Limiting sequence when we start with the positive integers (A000027) and delete in step n >= 1 the term at position n + tau(a(n)), where tau(k) is the number of divisors of k.
%H A136110 D. X. Charles, <a href="http://pages.cs.wisc.edu/~cdx/Sieve.pdf">Sieve Methods</a>, July 2000, University of Wisconsin.
%H A136110 Rémi Eismann, <a href="http://arXiv.org/abs/0711.0865">Decomposition into weight * level + jump and application to a new classification of primes</a>, arXiv:0711.0865 [math.NT]
%H A136110 M. C. Wunderlich, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa16/aa1614.pdf"> A general class of sieve generated sequences</a>, Acta Arithmetica XVI,1969, pp.41-56.
%H A136110 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%e A136110 First few steps are:
%e A136110 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
%e A136110 n = 1; delete term at position 1+tau(1) = 1+1 =2: 2;
%e A136110 1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
%e A136110 n = 2; delete term at position 2+tau(3) = 1+2 = 3: 5;
%e A136110 1,3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
%e A136110 n = 3; delete term at position 3+tau(4) = 3+3 = 6: 8;
%e A136110 1,3,4,6,7,9,10,11,12,13,14,15,16,17,18,19,20,...
%e A136110 n = 4; delete term at position 4+tau(6) = 4+4 = 8: 11;
%e A136110 1,3,4,6,7,9,10,12,13,14,15,16,17,18,19,20,...
%e A136110 n = 5; delete term at position 5+tau(7) = 5+2 = 7: 10;
%e A136110 1,3,4,6,7,9,12,13,14,15,16,17,18,19,20,...
%e A136110 n = 6; delete term at position 6+tau(9) = 6+3 = 9: 14;
%e A136110 1,3,4,6,7,9,12,13,15,16,17,18,19,20,...
%Y A136110 Cf. A000005 (number of divisors), A000027, A137292, A138899, A138900.
%K A136110 easy,nonn
%O A136110 1,2
%A A136110 _Ctibor O. Zizka_, Mar 16 2008
%E A136110 Edited and extended by _Klaus Brockhaus_, Apr 03 2008
%E A136110 Moved references to the Links section _R. J. Mathar_, Oct 23 2009