A122698 a(1)=a(2)=1 then a(n) = Sum_{d|n, 1

1, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Benoit Cloitre, Sep 22 2006

Keywords

• nonn
• easy
• mult

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..8192

Crossrefs

Cf. A000108.

Programs

Mathematica

a[1] = a[2] = 1; a[n_] := a[n] = DivisorSum[n, a[#] * a[n/#] &, 1 < # < n &]; Array[a, 100]
(* or *)
a[n_] := Module[{e = IntegerExponent[n, 2]}, If[n == 2^e, CatalanNumber[e-1], 0]]; a[1] = 1; a[n_?OddQ] = 0; Array[a, 100] (* Amiram Eldar, Sep 05 2023 *)

PARI

a(n)=if(n<3,1,sumdiv(n,d,if((d-1)*(d-n),a(d)*a(n/d),0)))

PARI

a(n)={my(e=valuation(n,2)); if(n==1<Andrew Howroyd, Aug 05 2018

Formula

a(1) = 1, for k>=0 a(2^(k+1)) = A000108(k) and if n>1 is not a power of 2 a(n) = 0.

Extensions

Keyword:mult added by Andrew Howroyd, Aug 05 2018