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

0,10

Links

Table of n, a(n) for n=0..70.

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}]

Crossrefs

Cf. A000607, A097356.

Sequence in context: A263799 A299230 A182576 * A128330 A133801 A372433

Adjacent sequences: A368866 A368867 A368868 * A368870 A368871 A368872

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 08 2024

Status

approved