OFFSET
1,4
COMMENTS
Total number of parts in all compositions (ordered partitions) of n into prime powers (1 excluded).
FORMULA
G.f.: Sum_{p prime, i>=1} x^(p^i) / (1 - Sum_{p prime, j>=1} x^(p^j))^2.
EXAMPLE
a(7) = 18 because we have [7], [5, 2], [4, 3], [3, 4], [3, 2, 2], [2, 5], [2, 3, 2], [2, 2, 3] and 1 + 2 + 2 + 2 + 3 + 2 + 3 + 3 = 18.
MATHEMATICA
nmax = 43; Rest[CoefficientList[Series[Sum[Floor[1/PrimeNu[i]] x^i, {i, 2, nmax}]/(1 - Sum[Floor[1/PrimeNu[j]] x^j, {j, 2, nmax}])^2, {x, 0, nmax}], x]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 31 2017
STATUS
approved