A070240 is duplicate of A007369

[David Wilson]

BTW, the sieve described in A070240 is a special case of a more general 
sieve.

Let D be a subset of N, and let f be an injection on D satisfying f(n) > n.

Define the sieve process as follows:

1.  Start with empty sequence S.
2.  Let E = D.
2.  Append the smallest element s of E to S.
3.  Remove s, f(s), f(f(s)), f(f(f(s))), ... from E.
4.  Go to 2.

After this sieving process, S = D - f(D).

In the case of A070240, f = sigma and D = {n | n >= 2}.

----- Original Message ----- 
From: "Max" <relf at unn.ac.ru>
To: <seqfan at ext.jussieu.fr>
Sent: Monday, August 08, 2005 6:40 PM
Subject: A070240 is duplicate of A007369


> First of all, I've verified the sequence A070240 and found that the 
> current last term "40" should not be present in the sequence.
> Second, it is easy to see that the procedure described at A070240 is 
> nothing more than just sieving the values of A007369 out of the sequence 
> of positive integers. It is very similar to the Sieve of Eratosthenes 
> sieving the prime numbers.
>
> So besides the first (artificially introduced) term "1", the sequence 
> A070240 is a duplicate of A007369.
> I think there is no much sense to keep it as a separate sequence.
>
> Max
>
>
>
> ID Number: A007369 (Formerly M1355)
> URL:       http://www.research.att.com/projects/OEIS?Anum=A007369
> Sequence:  2,5,9,10,11,16,17,19,21,22,23,25,26,27,29,33,34,35,37,41,43,
>            45,46,47,49,50,51,52,53,55,58,59,61,64,65,66,67,69,70,71,73,
>            75,76,77,79,81,82,83,85,86,87,88,89,92,94,95,97,99,100,101,
>            103,105,106,107,109,111,113
> Name:      Numbers n such that sigma (x) = n has no solution.
> References M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical
>               Functions, National Bureau of Standards Applied Math. Series 
> 55, 1964
>               (and various reprintings), p. 840.
> Example:   a(4) = 10 because there is no x < 10 whose sigma(x) = 10.
> Math'ca:   a = {}; Do[s = DivisorSigma[1, n]; a = Append[a, s], {n, 1, 
> 115} ];
>               Complement[ Table[ n, {n, 1, 115} ], Union[a] ]
> See also:  Sequence in context: A002580 A091656 A070240 this_sequence 
> A100530
>               A055394 A078360
>            Adjacent sequences: A007366 A007367 A007368 this_sequence 
> A007370
>               A007371 A007372
> Keywords:  nonn
> Offset:    1
> Author(s): njas, Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com)
> Extension: More terms from David Wison
>
> ID Number: A070240
> URL:       http://www.research.att.com/projects/OEIS?Anum=A070240
> Sequence:  1,2,5,9,10,11,16,17,19,21,22,23,25,26,27,29,33,34,35,37,40
> Name:      a(n) is constructed inductively in stages from the list L =
>               {1,2,3,....} by the following sieve procedure. Stage 1. Add 
> 1 as the
>               first term of the sequence a(n), and strike off 1 from L. 
> Stage n+1. Add
>               the first (i.e. leftmost) term k of L as a new term of the 
> sequence a(n),
>               and strike off k, sigma(k), sigma(sigma(k)),.... from L.
> See also:  Sequence in context: A020820 A002580 A091656 this_sequence 
> A007369
>               A100530 A055394
>            Adjacent sequences: A070237 A070238 A070239 this_sequence 
> A070241
>               A070242 A070243
> Keywords:  nonn
> Offset:    1
> Author(s): Joseph L. Pe (joseph_l_pe(AT)hotmail.com), May 08 2002
>