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Search: id:A128199
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| A128199 |
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a(n) = the number of primes S possible, if S = product of b(k)'s + product of c(k)'s, where the distinct positive integers <= n are partitioned into the two sets {b(k)} and {c(k)}. |
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3
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| 1, 1, 1, 2, 1, 3, 1, 3, 2, 0, 0, 3, 1, 4, 1, 2, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 2, 1, 1, 0, 2, 3, 2, 4, 2, 0, 0, 3, 1, 1, 2, 4, 4, 1, 5, 5, 5, 5, 4, 2, 0, 3, 4, 11, 4, 6, 8, 4, 4, 6, 6, 8, 6, 2, 2, 4, 4, 11, 7, 6, 13, 13, 19, 42, 15, 19, 14, 18, 19, 30, 38, 29, 12, 24, 24, 41, 15, 10, 12, 28, 19, 22, 27
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OFFSET
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0,4
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COMMENT
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a(0)=a(1)=1 because the product over the empty set is defined here as 1. For S to be a prime, the positive integers <= n, except 1 and the primes > n/2, must all be together in either {b(k)} or {c(k)}. If p is a prime where n/2 < p <= n, then it is possible that p is in either product of the S sum, as can 1.
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EXAMPLE
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For n = 5 we have the primes 23 = 1*2*4 + 3*5, 29 = 1*2*3*4 + 5, 43 = 1*2*4*5 + 3, so a(5)=3.
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MATHEMATICA
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f[n_] := Block[{d = Divisors[Times @@ Select[Range[n], PrimeQ[ # ] && 2# > n &]]}, Select[Union[d + n!/d], PrimeQ]]; Length /@ Array[f, 100, 0] (*Chandler*)
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CROSSREFS
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Cf. A127165, A127166.
Sequence in context: A130158 A104984 A083868 this_sequence A036459 A079167 A032741
Adjacent sequences: A128196 A128197 A128198 this_sequence A128200 A128201 A128202
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KEYWORD
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nonn
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AUTHOR
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Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 18 2007
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