login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A129233 Number of integers k>=n such that binomial(k,n) has fewer than n distinct prime factors. 3
1, 2, 6, 9, 20, 26, 43, 63, 75, 91, 130, 151, 185, 243, 279, 307, 383, 392, 488, 511, 595, 716, 904, 917, 1053, 1213, 1282, 1262, 1403, 1632, 1851, 1839, 1932, 2135, 2283, 2426, 2641, 2913, 3322, 3347, 3713, 3642, 4103, 4386, 4361, 4893, 5459 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
This sequence, which is much smoother than the closely related A005735, is calculated using the same "cheat" as described in Selmer's paper. That is, after we seem to have found the largest k for a given n, we search up to 10k for binomial coefficients having fewer than n distinct prime factors.
LINKS
Ernst S. Selmer, On the number of prime divisors of a binomial coefficient. Math. Scand. 39 (1976), no. 2, 271-281.
EXAMPLE
Consider n=3. The values of binomial(k,n) are 1,4,10,20,35,56,84,120 for k=3..10. Selmer shows that k=8 yields the largest value having fewer than 3 distinct prime factors. Factoring the other values shows that a(3)=6.
MATHEMATICA
Join[{1}, Table[cnt=1; n=k; b=1; n0=Infinity; While[n++; b=b*n/(n-k); If[Length[FactorInteger[b]]<k, cnt=cnt+1; n0=n]; n<10*n0]; cnt, {k, 2, 20}]]
CROSSREFS
Sequence in context: A182984 A301798 A093840 * A106529 A325040 A350949
KEYWORD
nonn
AUTHOR
T. D. Noe, Apr 05 2007, May 20 2007
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)