A085392 a(n) = largest prime divisor of n, or 1 if n is 1 or a prime.

1, 1, 1, 2, 1, 3, 1, 2, 3, 5, 1, 3, 1, 7, 5, 2, 1, 3, 1, 5, 7, 11, 1, 3, 5, 13, 3, 7, 1, 5, 1, 2, 11, 17, 7, 3, 1, 19, 13, 5, 1, 7, 1, 11, 5, 23, 1, 3, 7, 5, 17, 13, 1, 3, 11, 7, 19, 29, 1, 5, 1, 31, 7, 2, 13, 11, 1, 17, 23, 7, 1, 3, 1, 37, 5, 19, 11, 13, 1, 5, 3, 41, 1, 7, 17, 43, 29, 11, 1, 5, 13

Offset: 1

Author

Robert G. Wilson v and Reinhard Zumkeller, Jun 26 2003

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006530, A014673, A032742, A085393.

Programs

Haskell

a085392 = a006530 . a032742  -- Reinhard Zumkeller, Oct 03 2012

Maple

A085392 := proc(n) max( op(numtheory[divisors](n) minus {n})) ; A006530(%) ;
end proc:
seq(A085392(n),n=1..50) ; # R. J. Mathar, Jun 26 2011

Mathematica

PrimeFactors[n_] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; f[n_] := Block[{gpd = Divisors[n][[ -2]]}, If[gpd == 1, 1, PrimeFactors[gpd][[ -1]] ]]; Table[ If[n == 1, 1, f[n]], {n, 1, 95}]
Join[{1},Table[FactorInteger[Divisors[n][[-2]]][[-1,1]],{n,2,120}]] (* Harvey P. Dale, Jul 02 2019 *)
a[n_] := If[CompositeQ[n], FactorInteger[n][[-1, 1]], 1]; Array[a, 100] (* Amiram Eldar, Jun 19 2022 *)

PARI

gpd(n) = if (n==1, 1, n/factor(n)[1,1]);
gpf(n) = if (n==1, 1, vecmax(factor(n)[,1]));
a(n) = gpf(gpd(n)); \\ Michel Marcus, Apr 08 2018

Formula

a(n) = A006530(A032742(n)). - R. J. Mathar, Jun 26 2011

Extensions

Definition corrected by N. J. A. Sloane, Jul 02 2019. Also deleted an incorrect comment.