A321164 Sum of distinct products b_1*b_2*...*b_n where 1<=b_i<=n.

1, 7, 90, 1441, 38325, 916714, 37830100, 1194352181, 45241845825, 1951734678972, 147430334155104, 5664495439368403, 528359397843879784, 30798685780200874044, 1774211038440007650672, 99969666291681633988821, 13249072759407029981640765, 847264606120975715873578180

Offset: 1

Author

Seiichi Manyama, Jan 10 2019

Keywords

• nonn

Examples

			a(2) = 1 + 2 + 4 = 7.
a(3) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 27 = 90.
		

Crossrefs

Main diagonal of A321163.

Cf. A110713.

Programs

Maple

a:= proc(m) option remember; local b; b:=
      proc(n) option remember; `if`(n=0, {1},
        map(x-> seq(x*i, i=1..m), b(n-1)))
      end; forget(b); add(i, i=b(m))
    end:
seq(a(n), n=1..12);  # Alois P. Heinz, Jan 11 2019

Mathematica

a[m_] := a[m] = Module[{b}, b[n_] := b[n] = If[n==0, {1}, Map[Table[# i, {i, 1, m}]&, b[n-1]]] // Flatten // Union; b[m] // Total];
Array[a, 12] (* Jean-François Alcover, Nov 26 2020, after Alois P. Heinz *)

Extensions

a(15)-a(18) from Alois P. Heinz, Jan 11 2019