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.

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, 49, 51, 52, 55, 56, 58, 59, 62, 65, 66, 68, 70, 72, 73, 74, 78, 79, 80, 84, 85, 86, 88, 90, 92, 94, 96, 97, 98, 104, 105, 106, 108, 109, 111, 116, 118, 119, 121, 122, 126, 129, 130

Offset

1,2

Links

Table of n, a(n) for n=1..67.

D. X. Charles, Sieve Methods, July 2000, University of Wisconsin.

Rémi Eismann, Decomposition into weight * level + jump and application to a new classification of primes, arXiv:0711.0865 [math.NT]

M. C. Wunderlich, A general class of sieve generated sequences, Acta Arithmetica XVI,1969, pp.41-56.

Index entries for sequences generated by sieves

Example

First few steps are:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
n = 1; delete term at position 1+tau(1) = 1+1 =2: 2;
1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
n = 2; delete term at position 2+tau(3) = 1+2 = 3: 5;
1,3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,...
n = 3; delete term at position 3+tau(4) = 3+3 = 6: 8;
1,3,4,6,7,9,10,11,12,13,14,15,16,17,18,19,20,...
n = 4; delete term at position 4+tau(6) = 4+4 = 8: 11;
1,3,4,6,7,9,10,12,13,14,15,16,17,18,19,20,...
n = 5; delete term at position 5+tau(7) = 5+2 = 7: 10;
1,3,4,6,7,9,12,13,14,15,16,17,18,19,20,...
n = 6; delete term at position 6+tau(9) = 6+3 = 9: 14;
1,3,4,6,7,9,12,13,15,16,17,18,19,20,...

Crossrefs

Cf. A000005 (number of divisors), A000027, A137292, A138899, A138900.

Sequence in context: A201471 A338387 A360799 * A032725 A089038 A336175

Adjacent sequences: A136107 A136108 A136109 * A136111 A136112 A136113

Keyword

easy,nonn

Author

Ctibor O. Zizka, Mar 16 2008

Extensions

Edited and extended by Klaus Brockhaus, Apr 03 2008

Moved references to the Links section R. J. Mathar, Oct 23 2009

Status

approved