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

1,4

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

Links

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

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Left inverse of A253560.

Sequence in context: A009195 A072994 A332741 * A094521 A321757 A159272

Adjacent sequences: A052123 A052124 A052125 * A052127 A052128 A052129

Keyword

nonn,look

Author

James A. Sellers, Jan 21 2000

Status

approved