A309403 Total sum of the number of divisors of the element sum over all nonempty subsets of [n].

1, 5, 16, 40, 96, 217, 469, 1011, 2147, 4497, 9389, 19489, 40256, 82948, 170413, 349158, 714153, 1458199, 2972683, 6052561, 12308971, 25006177, 50755272, 102933086, 208594116, 422432018, 854956112, 1729360940, 3496259940, 7065053883, 14270420877, 28812580857

Offset: 1

Author

Alois P. Heinz, Jul 28 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..650

Crossrefs

Row sums of A309402.

Cf. A000005, A309281.

Programs

Maple

b:= proc(n, s) option remember; `if`(n=0,
      numtheory[tau](s), b(n-1, s)+b(n-1, s+n))
    end:
a:= n-> b(n, 0):
seq(a(n), n=1..30);

Mathematica

b[n_, s_] := b[n, s] = If[n == 0,
     If[s == 0, 0, DivisorSigma[0, s]], b[n-1, s] + b[n-1, s+n]];
a[n_] := b[n, 0];
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Mar 24 2022, after Alois P. Heinz *)