A368869 - OEIS

%I #6 Jan 15 2024 11:13:40

%S 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,

%T 21,23,24,25,27,28,29,31,32,34,35,37,38,40,42,43,45,47,150,158,166,

%U 175,183,193,202,212,222,232,243,254,265,277,289,301,314,327,340,354,368,383

%N Number of partitions of n into prime parts not greater than sqrt(n).

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p       b(n, i-1)+`if`(isprime(i), b(n-i, min(n-i, i)), 0)))

%p     end:

%p a:= n-> b(n, floor(sqrt(n))):

%p seq(a(n), n=0..70);  # _Alois P. Heinz_, Jan 13 2024

%t Table[SeriesCoefficient[Product[1/(1 - Boole[PrimeQ[k]] x^k), {k, 1, Floor[Sqrt[n]]}], {x, 0, n}], {n, 0, 70}]

%Y Cf. A000607, A097356.

%K nonn

%O 0,10

%A _Ilya Gutkovskiy_, Jan 08 2024