A133579 a(0)=a(1)=1; for n > 1, a(n) = 3*a(n-1) if a(n-1) and n are coprime, otherwise a(n) = a(n-1)/gcd(a(n-1), n).

1, 1, 3, 1, 3, 9, 3, 9, 27, 3, 9, 27, 9, 27, 81, 27, 81, 243, 27, 81, 243, 81, 243, 729, 243, 729, 2187, 81, 243, 729, 243, 729, 2187, 729, 2187, 6561, 729, 2187, 6561, 2187, 6561, 19683, 6561, 19683, 59049, 6561, 19683, 59049, 19683, 59049, 177147

Offset: 0

Author

Ctibor O. Zizka, Dec 26 2007

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A133058, A133580, A253092.

Programs

Maple

f:=proc(n) option remember;
if n <= 1 then 1
elif gcd(n,f(n-1))>1 then f(n-1)/gcd(n,f(n-1))
else 3*f(n-1); fi; end;
[seq(f(n),n=0..50)];
# N. J. A. Sloane, Feb 14 2015

Mathematica

nxt[{n_,a_}]:={n+1,If[CoprimeQ[a,n+1],3a,a/GCD[a,n+1]]}; Join[{1}, Transpose[ NestList[nxt,{1,1},50]][[2]]] (* Harvey P. Dale, Feb 14 2015 *)

PARI

A=vector(1000,i,1);for(n=2,#A,A[n]=if(gcd(A[n-1],n)>1,A[n-1]/gcd(A[n-1],n),A[n-1]*3)) \\ M. F. Hasler, Feb 15 2015

Extensions

Offset, definition, and terms corrected by N. J. A. Sloane, Feb 14 2015