A102787 Integer part of n#/((p-5)# 5#), where p=preceding prime to n.

0, 0, 0, 3, 2, 4, 7, 10, 14, 0, 29, 1, 50, 58, 67, 1, 1, 119, 2, 158, 172, 2, 218, 2, 3, 326, 346, 367, 388, 410, 4, 554, 4, 634, 4, 749, 5, 5, 907, 5, 5, 1079, 6, 1228, 1267, 1306, 7, 7, 1687, 1732, 1778, 7, 1919, 8, 8, 8, 8, 2429, 9, 2594, 2650, 9

Offset

2,4

Comments

0# = 1# = 2 by convention.

Links

Table of n, a(n) for n=2..63.

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 prime preceding n.

Prog

(PARI) c(n, r) = { local(p); forprime(p=r, 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: A158441 A349368 A376183 * A014193 A128885 A215335

Adjacent sequences: A102784 A102785 A102786 * A102788 A102789 A102790

Keyword

easy,nonn

Author

Cino Hilliard, Feb 25 2005

Status

approved