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

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, 6, 74, 52, 98, 54, 96, 56, 120, 98, 122, 102, 864, 104, 146, 150, 866, 150, 1584, 154, 938, 200, 1632, 246, 3072, 226, 1706, 990, 3864, 1038, 4560, 348, 3914, 1828, 4634, 1162, 7488

Offset

0,6

Links

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

Index entries for sequences related to compositions

Example

a(16) = 4 because we have [13, 3], [3, 13], [11, 5] and [5, 11].

Maple

b:= proc(n, i, p) option remember; `if`(n=0, irem(1+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[1 + 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, A184171, A219107, A332305, A339382, A339408, A339433.

Sequence in context: A023556 A238783 A044944 * A044945 A238005 A296509

Adjacent sequences: A339429 A339430 A339431 * A339433 A339434 A339435

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 04 2020

Status

approved