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Search: id:A119707
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| A119707 |
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Number of distinct primes appearing in all partitions of n into prime parts. |
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+0
1
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| 0, 1, 1, 1, 3, 2, 4, 3, 4, 4, 5, 4, 6, 5, 6, 6, 7, 6, 8, 7, 8, 8, 9, 8, 9, 9, 9, 9, 10, 9, 11, 10, 11, 11, 11, 11, 12, 11, 12, 12, 13, 12, 14, 13, 14, 14, 15, 14, 15, 15, 15, 15, 16, 15, 16, 16, 16, 16, 17, 16, 18, 17, 18, 18, 18, 18, 19, 18, 19, 19, 20, 19, 21, 20, 21, 21, 21, 21, 22
(list; graph; listen)
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OFFSET
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1,5
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FORMULA
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When n = odd and >=5 then a(n) = pi(n) = A000720(n). When n = even and >=4 then a(n) = pi(n-2) = A000720(n-2)
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EXAMPLE
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There is only 1 distinct prime number involved in the partitions of 4, namely 2 (in 2+2 = 4). The partition 3+1 does not count, as 1 is not a prime. So a(4)= 1.
There are 3 distinct primes involved in the partitions of 5 = 2+3, so a(5) = 3.
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MATHEMATICA
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f[n_] := If[OddQ@n, If[n == 3, 1, PrimePi@n], If[n == 2, 1, PrimePi[n - 2]]]; Array[f, 80] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A000720.
Adjacent sequences: A119704 A119705 A119706 this_sequence A119708 A119709 A119710
Sequence in context: A130079 A134559 A007456 this_sequence A052938 A140114 A025532
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KEYWORD
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nonn
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AUTHOR
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Anton Joha (antonjoha(AT)hotmail.com), Jun 10 2006
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(at)rgwv.com), Jun 15 2006
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