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A339432 Number of compositions (ordered partitions) of n into an even number of distinct primes.

%I A339432 #12 Feb 26 2022 04:57:03
%S A339432 1,0,0,0,0,2,0,2,2,2,2,0,2,2,2,2,4,24,4,2,4,26,4,48,6,50,28,48,28,72,
%T A339432 6,74,52,98,54,96,56,120,98,122,102,864,104,146,150,866,150,1584,154,
%U A339432 938,200,1632,246,3072,226,1706,990,3864,1038,4560,348,3914,1828,4634,1162,7488
%N A339432 Number of compositions (ordered partitions) of n into an even number of distinct primes.
%H A339432 Alois P. Heinz, <a href="/A339432/b339432.txt">Table of n, a(n) for n = 0..5000</a>
%H A339432 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%e A339432 a(16) = 4 because we have [13, 3], [3, 13], [11, 5] and [5, 11].
%p A339432 b:= proc(n, i, p) option remember; `if`(n=0, irem(1+p, 2)*p!, (s->
%p A339432      `if`(s>n, 0, b(n, i+1, p)+b(n-s, i+1, p+1)))(ithprime(i)))
%p A339432     end:
%p A339432 a:= n-> b(n, 1, 0):
%p A339432 seq(a(n), n=0..70);  # _Alois P. Heinz_, Dec 04 2020
%t A339432 b[n_, i_, p_] := b[n, i, p] = If[n == 0, Mod[1 + p, 2]*p!, Function[s, If[s > n, 0, b[n, i + 1, p] + b[n - s, i + 1, p + 1]]][Prime[i]]];
%t A339432 a[n_] := b[n, 1, 0];
%t A339432 Table[a[n], {n, 0, 70}] (* _Jean-François Alcover_, Feb 26 2022, after _Alois P. Heinz_ *)
%Y A339432 Cf. A000040, A184171, A219107, A332305, A339382, A339408, A339433.
%K A339432 nonn
%O A339432 0,6
%A A339432 _Ilya Gutkovskiy_, Dec 04 2020