A129233 -id:A129233 - cp's OEIS frontend

A005733 Least k such that binomial(k,n) has n or more distinct prime factors.

2, 4, 9, 10, 22, 26, 40, 50, 54, 55, 78, 115, 123, 154, 155, 209, 288, 220, 221, 292, 301, 378, 494, 494, 551, 715, 670, 786, 805, 803, 1079, 966, 1190, 1222, 1274, 1274, 1276, 1771, 1836, 1807, 1834, 2147, 2263, 2519, 2519, 3021, 3306, 3306, 3427, 3441, 3445

Offset: 1

N. J. A. Sloane

nonn

Table 3 in Selmer's paper has typos for n = 83, 100 and 117. - T. D. Noe, Apr 05 2007

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n=1..1000
Ernst S. Selmer, On the number of prime divisors of a binomial coefficient, Math. Scand. 39 (1976), no. 2, 271-281.

Cf. A005735, A129233.

Table[n=k; b=1; While[n++; b=b*n/(n-k); Length[FactorInteger[b]]T. D. Noe, Apr 05 2007 *)
lk[n_]:=Module[{k=n+1},While[PrimeNu[Binomial[k,n]]Harvey P. Dale, May 13 2018 *)

Edited by T. D. Noe, Apr 05 2007

A005735 Greatest k such that binomial(k,n) has fewer than n distinct prime factors.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

nonn

Table 2 in Selmer's paper has a typo for n = 76. Selmer "cheats" to find a(n) for n>27. - T. D. Noe, Apr 05 2007

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n=1..500
Ernst S. Selmer, On the number of prime divisors of a binomial coefficient, Math. Scand. 39 (1976), no. 2, 271-281.

Cf. A005733, A129233.

Join[{1}, Table[n=k; b=1; n0=Infinity; While[n++; b=b*n/(n-k); If[Length[FactorInteger[b]]T. D. Noe, Apr 05 2007 *)

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 26 2004

Edited by T. D. Noe, Apr 05 2007

cp's OEIS Frontend

A005733 Least k such that binomial(k,n) has n or more distinct prime factors.

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