A278617 Number of distinct odd primes less than or equal to 2n-3 that appear as a part in the partitions of 2n into two parts.

0, 0, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 8, 8, 9, 10, 10, 10, 11, 11, 12, 13, 13, 14, 14, 14, 15, 15, 15, 16, 17, 17, 17, 18, 18, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 23, 23, 24, 24, 25, 26, 26, 27, 28, 28, 29, 29, 29, 29, 29, 29, 29, 30, 30, 31, 31, 31

Offset: 1

Author

Wesley Ivan Hurt, Nov 23 2016

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A000720.

Essentially partial sums of A101264.

Programs

Magma

[0,0] cat [#PrimesUpTo(2*n-3)-1: n in [3..80]]; // Vincenzo Librandi, Nov 24 2016

Maple

with(numtheory): a:=n->`if`(n<3, 0, pi(2*n-3)-1): seq(a(n), n=1..100);

Mathematica

Table[If[n < 3, 0, PrimePi[2n - 3] - 1], {n, 100}]

Formula

a(n) = pi(2n - 3) - 1 for n > 2 with a(1) = a(2) = 0.