A280271 Expansion of (1/(1 - x))*Product_{k>=1} (1 + x^prime(k)).

1, 1, 2, 3, 3, 5, 5, 7, 8, 9, 11, 12, 14, 16, 18, 20, 23, 25, 29, 32, 36, 40, 44, 49, 54, 59, 65, 70, 76, 83, 89, 98, 105, 114, 123, 132, 143, 154, 165, 178, 190, 204, 219, 234, 251, 267, 285, 304, 324, 345, 368, 390, 415, 441, 468, 498, 527, 559, 591, 626, 663, 702, 742, 784, 828, 873, 923, 973, 1026, 1081, 1138

Offset: 0

Author

Ilya Gutkovskiy, Dec 30 2016

Keywords

• nonn

Comments

Partial sums of A000586.

Links

• Joerg Arndt, Matters Computational (The Fxtbook), end of section 16.4.2 "Partitions into distinct parts", pp.348ff
• Eric Weisstein's World of Mathematics, Prime Partition
• Index entries for related partition-counting sequences

Crossrefs

Cf. A000070, A000586, A034891, A036469.

Programs

Mathematica

nmax = 70; CoefficientList[Series[(1/(1 - x)) Product[(1 + x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: (1/(1 - x))*Product_{k>=1} (1 + x^prime(k)).