OFFSET
0,11
COMMENTS
Number of partitions of n into nonzero partial sums of primes (A007504).
LINKS
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 18 2017
STATUS
approved