A102789 Integer part of n#/((p-11)# 11#), where p=preceding prime to n.

0, 0, 0, 0, 0, 6, 7, 19, 41, 5, 8, 14, 20, 28, 1327, 46, 1, 82, 104, 125, 150, 177, 207, 252, 3, 4, 436, 46741, 52523, 58764, 0, 7, 986, 1079, 8, 9, 1529, 11, 1850, 2038, 13, 2426, 14, 15, 3143, 625601, 0, 0, 21, 5018, 1169257, 5520, 5809, 26, 27, 29, 30, 8299, 8741

Offset

2,6

Comments

0# = 1# = 2 by convention.

Links

Table of n, a(n) for n=2..60.

Formula

n# = product of primes <= n. 0#=1#=2. n#/((p-r)# r#) is analogous to the number of combinations of n things taken r at a time: C(n, r) = n!/((n-r)! r!) where factorial ! is replaced by primorial # and n is replaced with the preceding prime to n.

Prog

(PARI) c(n, r) = { local(p); forprime(p=2, n, print1(floor(primorial(p)/primorial(p-r)/primorial(r)+.0)", ") ) } primorial(n) = \ The product of primes <= n using the pari primelimit. { local(p1, x); if(n==0||n==1, return(2)); p1=1; forprime(x=2, n, p1*=x); return(p1) }

Crossrefs

Sequence in context: A028324 A074342 A329072 * A297556 A286969 A285913

Adjacent sequences: A102786 A102787 A102788 * A102790 A102791 A102792

Keyword

easy,nonn

Author

Cino Hilliard, Feb 25 2005

Status

approved