A281274 Expansion of Product_{j>=1} (1 + x^(Sum_{i=1..j} prime(i))).

1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 2, 0, 2, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 3, 0, 3, 0, 1, 2, 0, 2, 0, 0, 2, 1, 2, 1, 0, 2, 1, 3, 1, 2, 0, 2, 1, 1, 2, 0, 2, 1, 3, 2, 2, 1, 1, 2, 2, 2, 2, 0, 3, 0, 2, 2, 1, 4, 1, 3, 2, 3, 2, 2, 1, 2, 3

Offset

0,18

Comments

Number of partitions of n into distinct nonzero partial sums of primes (A007504).

Links

Table of n, a(n) for n=0..110.

Eric Weisstein's World of Mathematics, Prime Sums

Eric Weisstein's World of Mathematics, Prime Partition

Index entries for related partition-counting sequences

Formula

G.f.: Product_{j>=1} (1 + x^(Sum_{i=1..j} prime(i))).

Example

a(17) = 2 because we have [17] and [10, 5, 2], where 2 = prime(1), 5 = prime(1) + prime(2), 10 = prime(1) + prime(2) + prime(3), 17 = prime(1) + prime(2) + prime(3) + prime(4).

Mathematica

nmax = 110; CoefficientList[Series[Product[1 + x^Sum[Prime[i], {i, 1, j}], {j, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000586, A000607, A007504, A281273.

Sequence in context: A035145 A244315 A214303 * A191250 A107064 A113687

Adjacent sequences: A281271 A281272 A281273 * A281275 A281276 A281277

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 18 2017

Status

approved