A004788 Number of distinct prime divisors of the numbers in row n of Pascal's triangle.

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

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, n-1, 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: A194343 A071860 A358472 * A284523 A034584 A359357

Adjacent sequences: A004785 A004786 A004787 * A004789 A004790 A004791

Keyword

nonn

Author

Clark Kimberling

Status

approved