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A062760 a(n) is n divided by the largest power of the squarefree kernel of n (A007947) which divides it. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

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

LINKS

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

FORMULA

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

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 *)

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.

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

Sequence in context: A101446 A259396 A219093 * A014649 A279817 A253642

Adjacent sequences:  A062757 A062758 A062759 * A062761 A062762 A062763

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 16 2001

STATUS

approved

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Last modified February 19 09:28 EST 2018. Contains 299330 sequences. (Running on oeis4.)