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

1,12

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

Links

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

Formula

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

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

Example

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

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 *)

Prog

(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

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.

Sequence in context: A378222 A325355 A219093 * A323163 A322318 A014649

Adjacent sequences: A062757 A062758 A062759 * A062761 A062762 A062763

Keyword

nonn

Author

Labos Elemer, Jul 16 2001

Status

approved