A368870 Number of 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, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 37, 37, 40, 40, 44, 44, 48, 48, 52, 52, 56, 56, 61, 61, 65, 65, 70, 70, 75, 75, 80, 80, 85, 85, 91, 91, 96, 96, 351, 351, 378, 378, 411, 411, 441

Offset

0,17

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), 0, b(n-i, min(n-i, i)))))
    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. A002095, A097356.

Sequence in context: A243757 A321689 A369340 * A076568 A139259 A105444

Adjacent sequences: A368867 A368868 A368869 * A368871 A368872 A368873

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 08 2024

Status

approved