A368872 Number of compositions (ordered partitions) of n into prime parts not greater than sqrt(n).

1, 0, 0, 0, 1, 0, 1, 0, 1, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 2652, 3769, 5413, 7713, 11031, 15778, 22513, 32222, 46004, 65766, 94004, 134283, 191992, 274291, 392041, 560287, 800615, 1144320, 1635193, 2336976, 3339800, 4772784, 6821096

Offset

0,10

Links

Table of n, a(n) for n=0..47.

Maple

b:= proc(n, t) option remember; `if`(n=0, 1, add(
     `if`(isprime(j), b(n-j, t), 0), j=1..min(n, t)))
    end:
a:= n-> b(n, floor(sqrt(n))):
seq(a(n), n=0..47);  # Alois P. Heinz, Jan 13 2024

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[Boole[PrimeQ[k]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 47}]

Crossrefs

Cf. A023360, A364526.

Sequence in context: A159018 A361415 A345980 * A369221 A005427 A116024

Adjacent sequences: A368869 A368870 A368871 * A368873 A368874 A368875

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 08 2024

Status

approved