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A102787
Integer part of n#/((p-5)# 5#), where p=preceding prime to n.
0
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.
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
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Feb 25 2005
STATUS
approved