A052126 a(1) = 1; for n>1, a(n)=n/(largest prime dividing n).

1, 1, 1, 2, 1, 2, 1, 4, 3, 2, 1, 4, 1, 2, 3, 8, 1, 6, 1, 4, 3, 2, 1, 8, 5, 2, 9, 4, 1, 6, 1, 16, 3, 2, 5, 12, 1, 2, 3, 8, 1, 6, 1, 4, 9, 2, 1, 16, 7, 10, 3, 4, 1, 18, 5, 8, 3, 2, 1, 12, 1, 2, 9, 32, 5, 6, 1, 4, 3, 10, 1, 24, 1, 2, 15, 4, 7, 6, 1, 16, 27, 2, 1, 12, 5, 2, 3, 8, 1, 18, 7, 4, 3, 2, 5, 32, 1

Offset: 1

Author

James Sellers, Jan 21 2000

Keywords

• nonn
• look

Comments

For n>1, a(n)=1 if and only if n is prime. - Zak Seidov, Feb 09 2015

For n > 1, a(n) is the smallest divisor of n such that n/a(n) is prime. - David James Sycamore, Jan 03 2024

Examples

			a(15) = 15/(largest prime dividing 15) = 15/5 = 3.
		

Links

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

Crossrefs

Cf. A000040, A006530, A020639, A032742, A130065, A171462, A322820, A322826 (rgs-transform), A329697, A331410.

Left inverse of A253560.

Programs

Maple

a := n -> `if`(n=1, 1, n/max(numtheory[factorset](n)));
seq(a(n), n=1..97); # Peter Luschny, Jul 28 2014

Mathematica

a052126[n_] := Array[If[n == 1, 1, #/FactorInteger[#][[-1]][[1]]] &, n]; a052126[97] (* Michael De Vlieger, Dec 21 2014 *)

PARI

gpf(n)=my(f=factor(n)[,1]); f[#f]
a(n)=if(n<4,return(1)); n/gpf(n) \\ Charles R Greathouse IV, Apr 28 2015

Formula

a(n) = n/A006530(n).

a(n) = A130065(n)/A020639(n). - Reinhard Zumkeller, May 05 2007

a(A002110(n)) = A002110(n-1), a(p^k) = p^(k-1), p any prime; k >= 1. - David James Sycamore, Jan 03 2024

a(n) = n - A171462(n). - Antti Karttunen, Jan 04 2024