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A339433 Number of compositions (ordered partitions) of n into an odd number of distinct primes.

%I A339433 #11 Feb 26 2022 04:56:38
%S A339433 0,0,1,1,0,1,0,1,0,0,6,1,6,1,6,6,6,1,12,7,12,12,12,13,12,12,18,18,132,
%T A339433 19,132,25,18,24,252,30,258,31,264,156,486,37,498,157,504,276,738,175,
%U A339433 738,288,750,528,984,307,1218,666,1110,780,6378,679,6618,799,1716,1272
%N A339433 Number of compositions (ordered partitions) of n into an odd number of distinct primes.
%H A339433 Alois P. Heinz, <a href="/A339433/b339433.txt">Table of n, a(n) for n = 0..5000</a>
%H A339433 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%e A339433 a(10) = 6 because we have [5, 3, 2], [5, 2, 3], [3, 5, 2], [3, 2, 5], [2, 5, 3] and [2, 3, 5].
%p A339433 b:= proc(n, i, p) option remember; `if`(n=0, irem(p, 2)*p!, (s->
%p A339433      `if`(s>n, 0, b(n, i+1, p)+b(n-s, i+1, p+1)))(ithprime(i)))
%p A339433     end:
%p A339433 a:= n-> b(n, 1, 0):
%p A339433 seq(a(n), n=0..70);  # _Alois P. Heinz_, Dec 04 2020
%t A339433 b[n_, i_, p_] := b[n, i, p] = If[n == 0, Mod[p, 2]*p!, Function[s, If[s > n, 0, b[n, i + 1, p] + b[n - s, i + 1, p + 1]]][Prime[i]]];
%t A339433 a[n_] := b[n, 1, 0];
%t A339433 Table[a[n], {n, 0, 70}] (* _Jean-François Alcover_, Feb 26 2022, after _Alois P. Heinz_ *)
%Y A339433 Cf. A000040, A184172, A219107, A332304, A339383, A339409, A339432.
%K A339433 nonn
%O A339433 0,11
%A A339433 _Ilya Gutkovskiy_, Dec 04 2020