A113241 a(n) = Sum_{k=1..n} (tau(2*k) - 1).

0, 1, 3, 6, 9, 12, 17, 20, 24, 29, 34, 37, 44, 47, 52, 59, 64, 67, 75, 78, 85, 92, 97, 100, 109, 114, 119, 126, 133, 136, 147, 150, 156, 163, 168, 175, 186, 189, 194, 201, 210, 213, 224, 227, 234, 245, 250, 253, 264, 269, 277, 284, 291, 294, 305, 312, 321, 328

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

G.f.: (1/(1-x)) * Sum_{k>0} x^k*(1-x^(3*k))/((1-x^k)*(1-x^(2*k))).

a(n) = -n + Sum_{k=1..n} tau(2*k).

Maple

a:= proc(n) option remember; `if`(n<1, 0,
      a(n-1)+numtheory[tau](2*n)-1)
    end:
seq(a(n), n=0..57);  # Alois P. Heinz, Jun 16 2025

Mathematica

CoefficientList[ Series[ Sum[x^k(1 - x^(3k))/((1 - x^k)(1 - x^(2k))), {k, 60}], {x, 0, 57}]/(1 - x), x]

Crossrefs

Partial sums of A066660.

Cf. A000005.

Sequence in context: A186353 A362032 A061796 * A310153 A356104 A127621

Adjacent sequences: A113238 A113239 A113240 * A113242 A113243 A113244

Keyword

easy,nonn

Author

Paul Barry, Oct 19 2005

Extensions

More terms from Robert G. Wilson v, Oct 21 2005

Status

approved