A083730 Greatest prime^2 factor of n, or a(n)=1 for squarefree n.

1, 1, 1, 4, 1, 1, 1, 4, 9, 1, 1, 4, 1, 1, 1, 4, 1, 9, 1, 4, 1, 1, 1, 4, 25, 1, 9, 4, 1, 1, 1, 4, 1, 1, 1, 9, 1, 1, 1, 4, 1, 1, 1, 4, 9, 1, 1, 4, 49, 25, 1, 4, 1, 9, 1, 4, 1, 1, 1, 4, 1, 1, 9, 4, 1, 1, 1, 4, 1, 1, 1, 9, 1, 1, 25, 4, 1, 1, 1, 4, 9, 1, 1, 4, 1, 1, 1, 4, 1, 9, 1, 4, 1, 1, 1, 4, 1, 49, 9

Offset: 1

Author

Reinhard Zumkeller, Jun 14 2003

Keywords

• nonn
• easy

Comments

Not multiplicative, for example a(4)*a(9) <> a(36). - R. J. Mathar, Oct 31 2011

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006530, A001248, A005117, A013929, A008833, A046028, A249740.

Programs

Mathematica

a[n_] := If[(pos = Position[(f = FactorInteger[n])[[;; , 2]], ?(# >= 2 &)]) == {}, 1, f[[pos[[-1, 1]], 1]]^2];  Array[a, 100] (* _Amiram Eldar, Nov 14 2020 *)

PARI

a(n)=my(f=factor(n)); forstep(i=#f~,1,-1, if(f[i,2]>1, return(f[i,1]^2))); 1 \\ Charles R Greathouse IV, Jul 23 2017

Formula

a(n) = A249740(n)^2. - Amiram Eldar, Feb 11 2021