

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
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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
a(A004789(n)) = n and a(m) != n for m < A004789(n).  Reinhard Zumkeller, Mar 16 2015


LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000


FORMULA

a(n) = A001221(A001142(n)).  Reinhard Zumkeller, Mar 16 2015


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)
a004788 = a001221 . a001142  Reinhard Zumkeller, Mar 16 2015


CROSSREFS

Cf. A004789.
Cf. A001221, A001142, A256113.
Sequence in context: A078571 A194343 A071860 * A284523 A034584 A035430
Adjacent sequences: A004785 A004786 A004787 * A004789 A004790 A004791


KEYWORD

nonn


AUTHOR

Clark Kimberling


STATUS

approved



