A071854 a(n) = (number of distinct prime factors in C(2n,n)) - pi(n).

1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 2, 1, 2, 1, 2, 2, 2, 0, 1, 1, 1, 1, 3, 3, 2, 1, 2, 3, 3, 3, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 4, 5, 5, 4, 4, 4, 3, 4, 3, 3, 4, 4, 5, 5, 4, 5, 5, 5, 4, 4, 4, 5, 5, 5, 4, 4, 5, 6, 5, 5, 5, 6, 5, 4, 5, 6, 5, 6, 5, 6, 6

Offset: 1

Author

Benoit Cloitre, Jun 09 2002

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Programs

PARI

for(n=1,200,print1(omega(binomial(2*n,n))-sum(i=1,n,isprime(i)),","))

Formula

a(n) = A067434(n) - A000720(n)