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A341460 Number of partitions of n into 10 nonprime parts.

%I A341460 #11 Sep 01 2024 11:43:42
%S A341460 1,0,0,1,0,1,1,1,2,2,2,3,3,4,6,6,7,9,10,12,15,17,20,24,28,32,38,44,51,
%T A341460 60,68,79,92,104,122,139,157,181,208,234,270,304,347,391,445,499,569,
%U A341460 636,724,805,913,1015,1150,1274,1440,1592,1796,1980,2231,2455
%N A341460 Number of partitions of n into 10 nonprime parts.
%p A341460 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341460       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341460       `if`(isprime(i), 0, b(n-i, min(n-i, i), t-1))))
%p A341460     end:
%p A341460 a:= n-> b(n$2, 10):
%p A341460 seq(a(n), n=10..69);  # _Alois P. Heinz_, Feb 12 2021
%t A341460 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341460      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341460      If[PrimeQ[i], 0, b[n - i, Min[n - i, i], t - 1], 0]]];
%t A341460 a[n_] := b[n, n, 10];
%t A341460 Table[a[n], {n, 10, 69}] (* _Jean-François Alcover_, Feb 28 2022, after _Alois P. Heinz_ *)
%t A341460 Table[Count[IntegerPartitions[n,{10}],_?(NoneTrue[#,PrimeQ]&)],{n,10,70}] (* _Harvey P. Dale_, Sep 01 2024 *)
%Y A341460 Cf. A002095, A005171, A018252, A062610, A259201, A341408, A341451, A341452, A341453, A341454, A341455, A341457.
%K A341460 nonn
%O A341460 10,9
%A A341460 _Ilya Gutkovskiy_, Feb 12 2021