A281273 Expansion of Product_{j>=1} 1/(1 - x^(Sum_{i=1..j} prime(i))).

1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 3, 3, 4, 3, 4, 6, 4, 7, 4, 7, 7, 7, 9, 8, 9, 12, 9, 14, 10, 15, 14, 15, 17, 17, 18, 22, 19, 25, 21, 27, 27, 28, 31, 31, 33, 38, 36, 42, 39, 45, 47, 49, 52, 55, 55, 64, 61, 70, 67, 74, 77, 81, 84, 91, 89, 102, 98, 110, 109, 116, 123, 126, 133, 141, 141, 156, 153, 168, 169, 178, 188, 193

Offset

0,11

Comments

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

Links

Table of n, a(n) for n=0..86.

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

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/(1 - x^(Sum_{i=1..j} prime(i))).

Example

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

Mathematica

nmax = 86; CoefficientList[Series[Product[1/(1 - x^Sum[Prime[i], {i, 1, j}]), {j, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000586, A000607, A007504, A281274.

Sequence in context: A001319 A240833 A110919 * A109599 A333752 A066839

Adjacent sequences: A281270 A281271 A281272 * A281274 A281275 A281276

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 18 2017

Status

approved