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

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, 19, 132, 25, 18, 24, 252, 30, 258, 31, 264, 156, 486, 37, 498, 157, 504, 276, 738, 175, 738, 288, 750, 528, 984, 307, 1218, 666, 1110, 780, 6378, 679, 6618, 799, 1716, 1272

Offset: 0

Author

Ilya Gutkovskiy, Dec 04 2020

Keywords

• nonn

Examples

			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].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..5000
• Index entries for sequences related to compositions

Crossrefs

Cf. A000040, A184172, A219107, A332304, A339383, A339409, A339432.

Programs

Maple

b:= proc(n, i, p) option remember; `if`(n=0, irem(p, 2)*p!, (s->
     `if`(s>n, 0, b(n, i+1, p)+b(n-s, i+1, p+1)))(ithprime(i)))
    end:
a:= n-> b(n, 1, 0):
seq(a(n), n=0..70);  # Alois P. Heinz, Dec 04 2020

Mathematica

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]]];
a[n_] := b[n, 1, 0];
Table[a[n], {n, 0, 70}] (* Jean-François Alcover, Feb 26 2022, after Alois P. Heinz *)