/sci/ - Science & Math

here q(k) is the number of partitions of the integer k into distinct parts

http://mathworld.wolfram.com/PartitionFunctionQ.html

also for mathematica

Table[Sum[PartitionsQ[k], {k, 1, n}], {n, 1, 10}]

{1, 2, 4, 6, 9, 13, 18, 24, 32, 42}

why? I leave it to you as a combinatorial excercise :^)