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

0,11

Links

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Index entries for sequences related to compositions

Example

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].

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 *)

Crossrefs

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

Sequence in context: A010687 A176355 A109918 * A263494 A096956 A326126

Adjacent sequences: A339430 A339431 A339432 * A339434 A339435 A339436

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 04 2020

Status

approved