A294338 Number of ways to write n as a finite power-tower of positive integers greater than one, allowing both left and right nesting of parentheses.

1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1

Offset

1,4

Links

R. J. Mathar, Table of n, a(n) for n = 1..10000

Example

The a(16) = 5 ways are: 16, 4^2, (2^2)^2, 2^4, 2^(2^2).

Maple

A294338 := proc(n)
    local expo, g, a, d ;
    if n =1 then
        return 1;
    end if;
    # compute gcd of the set of prime power exponents (A052409)
    ifactors(n)[2] ;
    [ seq(op(2, ep), ep=%)] ;
    igcd(op(%)) ;
    # set of divisors of A052409 (without the 1)
    g := numtheory[divisors](%) minus {1} ;
    a := 0 ;
    for d in g do
        # recursive (sort of convolution) call
        a := a+ procname(d)*procname(root[d](n)) ;
    end do:
    1+a ;
end proc:
seq(A294338(n), n=1..120) ; # R. J. Mathar, Nov 27 2017

Mathematica

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

Crossrefs

Cf. A001597, A007916, A052409, A052410, A089723, A164336, A277562, A284639, A288636, A294336, A294337, A294339.

Sequence in context: A316782 A326647 A326028 * A316790 A316789 A319661

Adjacent sequences: A294335 A294336 A294337 * A294339 A294340 A294341

Keyword

nonn

Author

Gus Wiseman, Oct 28 2017

Status

approved