A072268 a(0)=1; a(n+1) = 1 + f(a(n))^2, where f(x) is the largest prime factor of x (A006530).

1, 2, 5, 26, 170, 290, 842, 177242, 160802, 2810, 78962, 9223370, 5033760602, 2935496262242, 2154284576409188208716642, 1379590379356276893461978662419832989306970202, 10320758390549056348725939119133160378521185060950774444682

Offset: 0

Author

Reinhard Zumkeller, Jul 08 2002

Keywords

• nonn

Comments

Is the sequence bounded?

Essentially the same as A031439; a(n) = A031439(n-1)^2 + 1. - Charles R Greathouse IV, May 08 2009

Examples

			Given a(5)=290: a(6) = 1 + lpf(a(5))^2 = 1 + lpf(290)^2 = 1 + 29^2 = 842.
		

Crossrefs

Cf. A031439.

Programs

Maple

with(numtheory): a[0]:=1: a[1]:=2: for n from 2 to 20 do b:=factorset(a[n-1]): a[n]:=1+op(nops(b),b)^2: od: seq(a[n],n=0..20); # Emeric Deutsch, Feb 05 2006

Mathematica

NestList[1+FactorInteger[#][[-1,1]]^2&,1,17] (* Harvey P. Dale, Feb 01 2022 *)

Extensions

More terms from Emeric Deutsch, Feb 05 2006

a(16) corrected by T. D. Noe, Nov 26 2007