A298602 Expansion of (1 - x)*Product_{k>=1} (1 - x^prime(k)).

1, -1, -1, 0, 1, 0, 0, 0, 1, 0, -1, -1, 1, 0, 0, 0, 1, -1, 0, -1, 1, 0, 0, -1, 2, 0, -1, -1, 1, -1, 1, -1, 2, 0, 0, -2, 2, -2, 0, 0, 3, -2, 1, -2, 2, -1, 0, -3, 5, -1, 0, -3, 3, -3, 3, -3, 3, -1, 2, -5, 6, -4, 1, -2, 6, -5, 3, -6, 5, -2, 4, -8, 9, -5, 3, -5, 7, -8, 7, -8, 8, -4, 5

Offset: 0

Author

Ilya Gutkovskiy, Jan 22 2018

Keywords

• sign

Comments

The difference between the number of partitions of n into an even number of distinct prime parts (including 1) and the number of partitions of n into an odd number of distinct prime parts (including 1).

Convolution inverse of A034891.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Index entries for related partition-counting sequences

Crossrefs

Cf. A000586, A000607, A034891, A036497, A046675 (partial sums).

Programs

Mathematica

nmax = 82; CoefficientList[Series[(1 - x) Product[(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

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