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

Author

Ilya Gutkovskiy, Jan 18 2017

Keywords

• nonn

Comments

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

Examples

			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).
		

Links

• Eric Weisstein's World of Mathematics, Prime Sums
• Eric Weisstein's World of Mathematics, Prime Partition
• Index entries for related partition-counting sequences

Crossrefs

Cf. A000586, A000607, A007504, A281273.

Programs

Mathematica

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

Formula

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