A371909 Number of divisors of the partial sums of A109890.

1, 2, 4, 6, 5, 8, 9, 6, 6, 12, 6, 9, 16, 15, 12, 14, 20, 16, 18, 15, 8, 12, 4, 8, 8, 8, 12, 16, 12, 8, 8, 12, 12, 16, 16, 8, 48, 8, 8, 8, 16, 20, 8, 16, 48, 12, 4, 16, 4, 12, 8, 8, 18, 16, 60, 12, 20, 8, 24, 24, 15, 36, 40, 36, 12, 8, 20, 32, 8, 12, 36, 16, 24

Offset: 1

Author

Michael De Vlieger, Apr 26 2024

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A109735, A109890, A371910.

Programs

Mathematica

nn = 120; c[_] := False;
Array[Set[{a[#], c[#]}, {#, True}] &, 2]; s = a[1] + a[2];
{1}~Join~Reap[Do[k = SelectFirst[Divisors[s], ! c[#] &];
     c[k] = True; Sow[DivisorSigma[0, s]];
     s += k, {n, 3, nn}] ][[-1, 1]]

Formula

a(n) = A000005(A109735(n)).