A370648 Number of ways to choose a subset s of [n] and then for each element in s choose a different prime factor.

1, 1, 2, 4, 6, 12, 22, 44, 56, 76, 130, 260, 376, 752, 1248, 1948, 2224, 4448, 5808, 11616, 16016, 24000, 38416, 76832, 94656, 114736, 181992, 204024, 274056, 548112, 743856, 1487712, 1593696, 2292992, 3590880, 4881120, 5630592, 11261184, 17559072, 24987360

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..140

Formula

a(p) = 2 * a(p-1) for prime p.

Maple

b:= proc(n, s) option remember; uses numtheory; `if`(n=0, 1, b(n-1, s)+
      add(b(n-1, select(x-> x<n, s union {j})), j=factorset(n) minus s))
    end:
a:= n-> b(n, {}):
seq(a(n), n=0..42);

Crossrefs

Cf. A000040, A370582.

Sequence in context: A196700 A283834 A341582 * A326114 A135231 A326489

Adjacent sequences: A370645 A370646 A370647 * A370649 A370650 A370651

Keyword

nonn

Author

Alois P. Heinz, Feb 25 2024

Status

approved