A025532 a(n) is the sum of exponents in the prime factorization of lcm{C(n,0), C(n,1), ..., C(n,n)}.

0, 0, 1, 1, 3, 2, 4, 3, 5, 5, 7, 5, 8, 7, 7, 6, 10, 8, 11, 9, 10, 10, 12, 9, 12, 12, 12, 12, 15, 13, 16, 13, 16, 16, 16, 14, 18, 17, 17, 15, 19, 17, 20, 18, 18, 19, 21, 17, 21, 20, 21, 20, 23, 20, 22, 20, 22, 22, 24, 21, 25, 24, 23, 21, 25, 24, 27, 25, 26, 25, 28, 24, 29, 28, 27

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Programs

Mathematica

{0, 0}~Join~Table[Total@ FactorInteger[LCM @@ Array[Binomial[n, #] &, n]][[All, -1]], {n, 2, 74}] (* Michael De Vlieger, Jan 13 2018 *)

PARI

for(n=0, 100, l=1; for(k=0, n, l=lcm(l,binomial(n,k))); v=factor(l); s=0; for(k=1, matsize(v)[1], s=s+v[k,2]); print1(s","))

PARI

a(n) = bigomega(lcm(vector(n+1, k, binomial(n, k-1)))); \\ Michel Marcus, Jan 06 2018

Formula

a(n) = A025528(n + 1) - A001222(n + 1). - Luc Rousseau, Jan 04 2018

a(n) = A001222(A002944(n+1)). - Michel Marcus, Jan 05 2018

Extensions

More terms from Ralf Stephan, Mar 28 2003