A005733 Least k such that binomial(k,n) has n or more distinct prime factors. (Formerly M1166)

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

1,1

Comments

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

References

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

Links

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.

Mathematica

Table[n=k; b=1; While[n++; b=b*n/(n-k); Length[FactorInteger[b]]<k]; n, {k, 100}] (* T. D. Noe, Apr 05 2007 *)
lk[n_]:=Module[{k=n+1}, While[PrimeNu[Binomial[k, n]]<n, k++]; k]; Array[ lk, 60] (* Harvey P. Dale, May 13 2018 *)

Crossrefs

Cf. A005735, A129233.

Sequence in context: A060756 A075347 A352506 * A096692 A203847 A365811

Adjacent sequences: A005730 A005731 A005732 * A005734 A005735 A005736

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

Edited by T. D. Noe, Apr 05 2007

Status

approved