A062962 Number of divisors of n-th term of sequence a(n+1) = a(n)*(a(0) + ... + a(n)) (A001697).

1, 1, 2, 4, 12, 40, 160, 792, 9408, 783360, 55987200, 35610624000, 269007298560000

Offset: 0

Author

Jason Earls, Jul 22 2001

Keywords

• nonn
• hard
• more

Crossrefs

Cf. A000005, A001697.

Programs

Mathematica

a[0] = 1; a[1] = 1; a[n_] := a[n] = a[n - 1]^2*(1 + 1/a[n - 2]); Table[DivisorSigma[0, a[n]], {n, 0, 10}]  (* Amiram Eldar, Feb 17 2019 after Jean-François Alcover at A001697 *)

PARI

a(n)=if(n<2,n >= 0,a(n-1)^2*(1+1/a(n-2)));
for(n=0,11,print1(numdiv(a(n)), ", "))

Formula

a(n) = A000005(A001697(n)). - Amiram Eldar, Feb 17 2019

Extensions

a(11) from Amiram Eldar, Feb 17 2019

a(12) from Max Alekseyev, Feb 20 2024