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A005735
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Greatest k such that binomial(k,n) has fewer than n distinct prime factors.
(Formerly M2719)
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3
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1, 3, 8, 14, 32, 62, 87, 169, 132, 367, 389, 510, 394, 512, 512, 1880, 1880, 1882, 2099, 1879, 1885, 2102, 3470, 3470, 4805, 4806, 4806, 3475, 4806, 4938, 4939, 5108, 5119, 6271, 5122, 5869, 10663, 10663, 10663, 7421, 10667, 10667, 10668, 11710, 11711
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Table 2 in Selmer's paper has a typo for n = 76. Selmer "cheats" to find a(n) for n>27. - T. D. Noe (noe(AT)sspectra.com), Apr 05 2007
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REFERENCES
| Selmer, Ernst S.; On the number of prime divisors of a binomial coefficient. Math. Scand. 39 (1976), no. 2, 271-281.
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..500
Selmer, Ernst S.; On the number of prime divisors of a binomial coefficient. Math. Scand. 39 (1976), no. 2, 271-281.
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MATHEMATICA
| Join[{1}, Table[n=k; b=1; n0=Infinity; While[n++; b=b*n/(n-k); If[Length[FactorInteger[b]]<k, n0=n]; n<10*n0]; n0, {k, 2, 30}]] - T. D. Noe (noe(AT)sspectra.com), Apr 05 2007
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CROSSREFS
| Cf. A005733, A129233.
Sequence in context: A169929 A129067 A168155 * A135872 A045263 A004733
Adjacent sequences: A005732 A005733 A005734 * A005736 A005737 A005738
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Pab Ter (pabrlos(AT)yahoo.com), May 26 2004
Edited by T. D. Noe (noe(AT)sspectra.com), Apr 05 2007
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