A307305 Self-composition of the number of divisors function (A000005).

1, 4, 12, 34, 92, 246, 640, 1660, 4264, 10914, 27732, 70247, 177466, 447570, 1126344, 2828465, 7089391, 17746456, 44384884, 110927184, 276993616, 691007612, 1722214602, 4289021667, 10675557184, 26561494820, 66063726382, 164248795485, 408168287028, 1013819012498

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..760

Eric Weisstein's World of Mathematics, Divisor Function

Formula

G.f.: g(g(x)), where g(x) = Sum_{k>=1} x^k/(1 - x^k) is the g.f. of A000005.

Mathematica

g[x_] := g[x] = Sum[x^k/(1 - x^k), {k, 1, 30}]; a[n_] := a[n] = SeriesCoefficient[g[g[x]], {x, 0, n}]; Table[a[n], {n, 30}]

Crossrefs

Cf. A000005, A010553, A055507, A307306.

Sequence in context: A191823 A110335 A166294 * A176753 A248873 A180224

Adjacent sequences: A307302 A307303 A307304 * A307306 A307307 A307308

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 01 2019

Status

approved