A368869 Number of partitions of n into prime parts not greater than sqrt(n).

1, 0, 0, 0, 1, 0, 1, 0, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 3, 4, 4, 4, 4, 5, 15, 16, 17, 18, 19, 21, 21, 23, 24, 25, 27, 28, 29, 31, 32, 34, 35, 37, 38, 40, 42, 43, 45, 47, 150, 158, 166, 175, 183, 193, 202, 212, 222, 232, 243, 254, 265, 277, 289, 301, 314, 327, 340, 354, 368, 383

Offset: 0

Author

Ilya Gutkovskiy, Jan 08 2024

Keywords

• nonn

Crossrefs

Cf. A000607, A097356.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1)+`if`(isprime(i), b(n-i, min(n-i, i)), 0)))
    end:
a:= n-> b(n, floor(sqrt(n))):
seq(a(n), n=0..70);  # Alois P. Heinz, Jan 13 2024

Mathematica

Table[SeriesCoefficient[Product[1/(1 - Boole[PrimeQ[k]] x^k), {k, 1, Floor[Sqrt[n]]}], {x, 0, n}], {n, 0, 70}]