A368873 Number of compositions (ordered partitions) of n into nonprime parts not greater than sqrt(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 95, 131, 181, 250, 345, 476, 657, 907, 1252, 1728, 2385, 3292, 4544, 6272, 8657, 11949, 16493, 22765, 31422, 43371, 439373, 643932, 943728, 1383100, 2027032, 2970760, 4353861, 6380893, 9351653, 13705513, 20086406, 29438059

Offset: 0

Author

Ilya Gutkovskiy, Jan 08 2024

Keywords

• nonn

Crossrefs

Cf. A052284, A364526.

Programs

Maple

b:= proc(n, t) option remember; `if`(n=0, 1, add(
     `if`(isprime(j), 0, b(n-j, t)), 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}]