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A119707 Number of distinct primes appearing in all partitions of n into prime parts. 0
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; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..79.

FORMULA

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)

EXAMPLE

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.

MATHEMATICA

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 *)

CROSSREFS

Cf. A000720.

Sequence in context: A243289 A134559 A007456 * A052938 A140114 A243852

Adjacent sequences:  A119704 A119705 A119706 * A119708 A119709 A119710

KEYWORD

nonn

AUTHOR

Anton Joha, Jun 10 2006

EXTENSIONS

Edited and extended by Robert G. Wilson v, Jun 15 2006

STATUS

approved

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Last modified May 25 04:36 EDT 2017. Contains 287008 sequences.