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A007369
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Numbers n such that sigma (x) = n has no solution.
(Formerly M1355)
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23
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| With an initial 1, may be 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. - Joseph L. Pe (joseph_l_pe(AT)hotmail.com), May 08 2002
This sieve 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). To get the current sequence, take f = sigma and D = {n | n >= 2}. - Max Alekseyev (maxale(AT)gmail.com), Aug 08 2005
a(n) = numbers k in increasing order such that A000203(m) = k has no solution, where A000203(m) = sum of divisors of m. Complement of A002191. A175192(a(n)) = 0, A054973(a(n)) = 0. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 01 2010]
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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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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EXAMPLE
| a(4) = 10 because there is no x < 10 whose sigma(x) = 10.
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MATHEMATICA
| a = {}; Do[s = DivisorSigma[1, n]; a = Append[a, s], {n, 1, 115} ]; Complement[ Table[ n, {n, 1, 115} ], Union[a] ]
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CROSSREFS
| Sequence in context: A133508 A125969 A070240 * A100530 A155469 A055394
Adjacent sequences: A007366 A007367 A007368 * A007370 A007371 A007372
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
| More terms from David Wison
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