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

%I A321164 #21 Nov 26 2020 09:15:59
%S A321164 1,7,90,1441,38325,916714,37830100,1194352181,45241845825,
%T A321164 1951734678972,147430334155104,5664495439368403,528359397843879784,
%U A321164 30798685780200874044,1774211038440007650672,99969666291681633988821,13249072759407029981640765,847264606120975715873578180
%N A321164 Sum of distinct products b_1*b_2*...*b_n where 1<=b_i<=n.
%e A321164 a(2) = 1 + 2 + 4 = 7.
%e A321164 a(3) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 27 = 90.
%p A321164 a:= proc(m) option remember; local b; b:=
%p A321164       proc(n) option remember; `if`(n=0, {1},
%p A321164         map(x-> seq(x*i, i=1..m), b(n-1)))
%p A321164       end; forget(b); add(i, i=b(m))
%p A321164     end:
%p A321164 seq(a(n), n=1..12);  # _Alois P. Heinz_, Jan 11 2019
%t A321164 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];
%t A321164 Array[a, 12] (* _Jean-François Alcover_, Nov 26 2020, after _Alois P. Heinz_ *)
%Y A321164 Main diagonal of A321163.
%Y A321164 Cf. A110713.
%K A321164 nonn
%O A321164 1,2
%A A321164 _Seiichi Manyama_, Jan 10 2019
%E A321164 a(15)-a(18) from _Alois P. Heinz_, Jan 11 2019