login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A307305
Self-composition of the number of divisors function (A000005).
2
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 01 2019
STATUS
approved