This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(14) = 5 because we have [14], [10, 4], [8, 6], [6, 8] and [4, 10].
b:= proc(n, t) option remember;
`if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
`if`(isprime(j), 0, b(n-j, t-1)), j=1..n)))
end:
a:= n-> b(n, 10):
seq(a(n), n=10..50); # Alois P. Heinz, Feb 13 2021
nmax = 50; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^10, {x, 0, nmax}], x] // Drop[#, 10] &
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
Table[SeriesCoefficient[1/(1 - Sum[Boole[!PrimeQ[k]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 47}]