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
Keywords
Examples
a(16) = 4 because we have [13, 3], [3, 13], [11, 5] and [5, 11].
Links
Programs
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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 *)