OFFSET
0,3
COMMENTS
Number of subsets of [n] in which exactly half of the elements are primes: a(6) = 20: {}, {1,2}, {1,3}, {1,5}, {2,4}, {2,6}, {3,4}, {3,6}, {4,5}, {5,6}, {1,2,3,4}, {1,2,3,6}, {1,2,4,5}, {1,2,5,6}, {1,3,4,5}, {1,3,5,6}, {2,3,4,6}, {2,4,5,6}, {3,4,5,6}, {1,2,3,4,5,6}. - Alois P. Heinz, Oct 11 2022
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..2000 (terms n = 1..1000 from Vincenzo Librandi)
FORMULA
a(n) = C(n,pi(n)).
EXAMPLE
C(16,6) = 8008.
MAPLE
with(numtheory); A037031:=n->binomial(n, pi(n)); seq(A037031(k), k=0..100); # Wesley Ivan Hurt, Oct 19 2013
MATHEMATICA
Table[Binomial[n, PrimePi[n]], {n, 40}] (* Harvey P. Dale, Mar 22 2012 *)
PROG
(Python)
from math import comb
from sympy import primepi
def A037031(n): return comb(n, primepi(n)) # Chai Wah Wu, Oct 14 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Oct 11 2022
STATUS
approved