

A004788


Number of distinct prime divisors of the numbers in row n of Pascal's triangle.


6



0, 0, 1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 9, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 13, 13, 14, 13, 14, 15, 14, 14, 14, 14, 15, 15, 15, 16, 15, 15, 16, 17, 17, 17, 18, 17, 17, 17, 18, 18, 18, 19, 19, 20, 20
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,5


COMMENTS

Also the number of prime divisors of A002944(n) = lcm_{j=0..floor(n/2)} binomial(n,j).
The terms are increasing by intervals, then decrease once. The local maxima are obtained for 23, 44, 47, 55, 62, 79, 83, 89, 104, 119, 131, 134, 139, 143, ....  Michel Marcus, Mar 21 2013


LINKS



FORMULA



MATHEMATICA

Table[prd = Product[Binomial[n, k], {k, 0, n}]; If[prd == 1, 0, Length[FactorInteger[prd]]], {n, 0, 100}] (* T. D. Noe, Mar 21 2013 *)


PROG

(PARI) a(n) = {sfp = Set(); for (k=1, n1, sfp = setunion(sfp, Set(factor(binomial(n, k))[, 1]))); return (length(sfp)); } \\ Michel Marcus, Mar 21 2013
(Haskell)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



