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

0,2

Comments

Is the sequence bounded?

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

Links

Table of n, a(n) for n=0..16.

Example

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

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 *)

Crossrefs

Cf. A031439.

Sequence in context: A226170 A371614 A334639 * A019014 A128595 A358715

Adjacent sequences: A072265 A072266 A072267 * A072269 A072270 A072271

Keyword

nonn

Author

Reinhard Zumkeller, Jul 08 2002

Extensions

More terms from Emeric Deutsch, Feb 05 2006

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

Status

approved