A119707 - OEIS

A119707

Number of distinct primes appearing in all partitions of n into prime parts.

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(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: A333773 A007456 A316141 * A377298 A354679 A307118

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