A062760 a(n) is n divided by the largest power of the squarefree kernel of n (A007947) which divides it.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 3, 1, 1, 8, 1, 5, 1, 2, 1, 9, 1, 4, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 5, 2, 1, 1, 1, 8, 1, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 16, 1, 7, 3, 1, 1, 1, 1, 4

Offset: 1

Author

Labos Elemer, Jul 16 2001

Keywords

• nonn

Comments

a(n) divides A003557 but is not equal to it.

a(n) is least d such that the prime power exponents of n/d are all equal; see also A066636. - David James Sycamore, Jun 13 2024

Examples

			n=1800: the squarefree kernel is 2*3*5 = 30 and 900 = 30^2 divides n, a(1800) = 2, the quotient of 1800/900.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001694, A003557, A007947, A051904, A003557, A052485, A062759.

Cf. A059404 (n such that a(n)>1), A072774 (n such that a(n)=1).

Cf. A066636.

Programs

Maple

f:= proc(n) local F,m,t;
  F:= ifactors(n)[2];
  m:= min(seq(t[2],t=F));
  mul(t[1]^(t[2]-m),t=F)
end proc:
map(f, [$1..200]); # Robert Israel, Nov 03 2017

Mathematica

{1}~Join~Table[n/#^IntegerExponent[n, #] &@ Last@ Select[Divisors@ n, SquareFreeQ], {n, 2, 104}] (* Michael De Vlieger, Nov 02 2017 *)
a[n_] := Module[{f = FactorInteger[n], e}, e = Min[f[[;; , 2]]]; f[[;; , 2]] -= e; Times @@ Power @@@ f]; Array[a, 100] (* Amiram Eldar, Feb 12 2023 *)

PARI

A007947(n) = factorback(factorint(n)[, 1]); \\ Andrew Lelechenko, May 09 2014
A051904(n) = if(1==n,0,vecmin(factor(n)[, 2])); \\ After Charles R Greathouse IV's code
A062760(n) = n/(A007947(n)^A051904(n)); \\ Antti Karttunen, Sep 23 2017

Formula

a(n) = n/(A007947(n)^A051904(n)).

a(n) = n/A062759(n). - Amiram Eldar, Feb 12 2023