OFFSET
0,5
FORMULA
EXAMPLE
a(6) = 5 because we have [5, 1], [3, 3], [3, 1, 1, 1], [2, 2, 1, 1] and [1, 1, 1, 1, 1, 1].
MAPLE
b:= proc(n, i, t) option remember; (p->
`if`(n=0, t, `if`(i<0, 0, b(n, i-1, t)+
`if`(p>n, 0, b(n-p, i, 1-t)))))(`if`(i<1, 1, ithprime(i)))
end:
a:= n-> b(n, numtheory[pi](n), 1):
seq(a(n), n=0..60); # Alois P. Heinz, Dec 02 2020
MATHEMATICA
nmax = 55; CoefficientList[Series[(1/2) ((1/(1 - x)) Product[1/(1 - x^Prime[k]), {k, 1, nmax}] + (1/(1 + x)) Product[1/(1 + x^Prime[k]), {k, 1, nmax}]), {x, 0, nmax}], x]
Table[Count[(Boole[PrimeQ/@(IntegerPartitions[n]/.(1->2))]), _?(EvenQ[Length[#]] && FreeQ[ #, 0]&)], {n, 0, 60}] (* Harvey P. Dale, Aug 20 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 02 2020
STATUS
approved