

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
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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(n2) = A000720(n2)


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: A333773 A007456 A316141 * A307118 A052938 A302391
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



