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A102788
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Integer part of n#/((p-7)# 7#), where p=preceding prime to n.
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0
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0, 0, 0, 0, 1, 4, 11, 19, 35, 3, 4, 5, 7, 310, 394, 11, 14, 17, 19, 22, 1653, 27, 31, 35, 0, 46, 4805, 5300, 5720, 6275, 0, 79, 85, 90, 0, 107, 112, 121, 129, 137, 147, 154, 0, 175, 34581, 36029, 1, 1, 241, 55200, 57676, 265, 274, 1, 307, 321, 336, 347, 357, 370
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OFFSET
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2,6
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COMMENTS
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0# = 1# = 2 by convention.
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LINKS
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FORMULA
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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.
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PROG
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(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) }
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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