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Total sum of the number of divisors of the element sum over all nonempty subsets of [n].
3

%I #13 Mar 24 2022 03:58:59

%S 1,5,16,40,96,217,469,1011,2147,4497,9389,19489,40256,82948,170413,

%T 349158,714153,1458199,2972683,6052561,12308971,25006177,50755272,

%U 102933086,208594116,422432018,854956112,1729360940,3496259940,7065053883,14270420877,28812580857

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

%H Alois P. Heinz, <a href="/A309403/b309403.txt">Table of n, a(n) for n = 1..650</a>

%p b:= proc(n, s) option remember; `if`(n=0,

%p numtheory[tau](s), b(n-1, s)+b(n-1, s+n))

%p end:

%p a:= n-> b(n, 0):

%p seq(a(n), n=1..30);

%t b[n_, s_] := b[n, s] = If[n == 0,

%t If[s == 0, 0, DivisorSigma[0, s]], b[n-1, s] + b[n-1, s+n]];

%t a[n_] := b[n, 0];

%t Table[a[n], {n, 1, 30}] (* _Jean-François Alcover_, Mar 24 2022, after _Alois P. Heinz_ *)

%Y Row sums of A309402.

%Y Cf. A000005, A309281.

%K nonn

%O 1,2

%A _Alois P. Heinz_, Jul 28 2019