A294339 Number of ways to write 2^n as a finite power-tower of positive integers greater than one, allowing both left and right nesting of parentheses.

1, 2, 2, 5, 2, 6, 2, 12, 5, 6, 2, 19, 2, 6, 6, 32, 2, 19, 2, 19, 6, 6, 2, 56, 5, 6, 12, 19, 2, 26, 2, 79, 6, 6, 6, 71, 2, 6, 6, 56, 2, 26, 2, 19, 19, 6, 2, 169, 5, 19, 6, 19, 2, 56, 6, 56, 6, 6, 2, 101, 2, 6, 19, 203, 6, 26, 2, 19, 6, 26, 2, 237, 2, 6, 19, 19

Offset

1,2

Links

Hans Havermann, Table of n, a(n) for n = 1..10000

Formula

a(n) = A294338(2^n). - R. J. Mathar, Nov 27 2017

Example

The a(6) = 6 ways are 64, 8^2, (2^3)^2, 4^3, (2^2)^3, 2^6.

Maple

f:= proc(n) option remember; local F, t, s, g, a;
  F:= ifactors(n)[2];
  g:= igcd(op(map(t -> t[2], F)));
  t:= 1;
  for s in numtheory:-divisors(g) minus {1} do
    t:= t + procname(mul(a[1]^(a[2]/s), a=F))*procname(s)
  od;
  t
end proc:
seq(f(2^n), n=1..100); # Robert Israel, Dec 01 2017

Mathematica

a[n_]:=1+Sum[a[n^(1/g)]*a[g], {g, Rest[Divisors[GCD@@FactorInteger[n][[All, 2]]]]}];
Table[a[2^n], {n, 100}]

Crossrefs

Cf. A001055, A001597, A007916, A052409, A052410, A089723, A164336, A277562, A284639, A288636, A294336, A294337, A294338.

Sequence in context: A299764 A301830 A305799 * A185291 A018216 A059907

Adjacent sequences: A294336 A294337 A294338 * A294340 A294341 A294342

Keyword

nonn

Author

Gus Wiseman, Oct 28 2017

Status

approved