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A281274 Expansion of Product_{j>=1} (1 + x^(Sum_{i=1..j} prime(i))). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 16 03:57 EDT 2018. Contains 316259 sequences. (Running on oeis4.)