OFFSET
1,2
COMMENTS
Sum of all parts of all partitions of n into distinct primes.
LINKS
Eric Weisstein's World of Mathematics, Prime Partition
FORMULA
G.f.: Sum_{k>=1} prime(k)*x^prime(k)/(1 + x^prime(k)) * Product_{k>=1} (1 + x^prime(k)).
G.f.: x*f'(x), where f(x) = Product_{k>=1} (1 + x^prime(k)).
a(n) = n*A000586(n).
EXAMPLE
a(12) = 24 because we have [7, 5], [7, 3, 2] and 2*12 = 24.
MATHEMATICA
nmax = 65; Rest[CoefficientList[Series[Sum[Prime[k] x^Prime[k]/(1 + x^Prime[k]), {k, 1, nmax}] Product[1 + x^Prime[k], {k, 1, nmax}], {x, 0, nmax}], x]]
nmax = 65; Rest[CoefficientList[Series[x D[Product[1 + x^Prime[k], {k, 1, nmax}], x], {x, 0, nmax}], x]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 11 2017
STATUS
approved