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

Author

Ilya Gutkovskiy, Apr 01 2019

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..760
• Eric Weisstein's World of Mathematics, Divisor Function

Crossrefs

Cf. A000005, A010553, A055507, A307306.

Programs

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}]

Formula

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