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A085731 Greatest common divisor of n and its arithmetic derivative. 13
1, 1, 1, 4, 1, 1, 1, 4, 3, 1, 1, 4, 1, 1, 1, 16, 1, 3, 1, 4, 1, 1, 1, 4, 5, 1, 27, 4, 1, 1, 1, 16, 1, 1, 1, 12, 1, 1, 1, 4, 1, 1, 1, 4, 3, 1, 1, 16, 7, 5, 1, 4, 1, 27, 1, 4, 1, 1, 1, 4, 1, 1, 3, 64, 1, 1, 1, 4, 1, 1, 1, 12, 1, 1, 5, 4, 1, 1, 1, 16, 27, 1, 1, 4, 1, 1, 1, 4, 1, 3, 1, 4, 1, 1, 1, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) = GCD(n, A003415(n));

a(n) = 1 iff n is squarefree (A005117), cf. A068328.

This sequence is very probably multiplicative. - Mitch Harris, Apr 19 2005

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

Victor Ufnarovski and Bo Ahlander, How to Differentiate a Number, J. Integer Seqs., Vol. 6, 2003, #03.3.4.

FORMULA

Multiplicative with a(p^e) = p^e if p divides e; a(p^e) = p^(e-1) otherwise. - Eric M. Schmidt, Oct 22 2013

MAPLE

A085731:= proc(n)

local a, p, pfs;

  if n<=1 then a:=0;

    else pfs:=ifactors(n)[2]; a:=n*add(op(2, p)/op(1, p), p=pfs);

  fi;

  igcd(n, a);

end proc:

seq(A085731(n), n=1..100) ; # Paolo P. Lava, Apr 14 2011

MATHEMATICA

d[0] = d[1] = 0; d[n_] := d[n] = n*Total[Apply[#2/#1 &, FactorInteger[n], {1}]]; a[n_] := GCD[n, d[n]]; Table[a[n], {n, 1, 96}] (* Jean-Fran├žois Alcover, Feb 21 2014 *)

PROG

(Haskell)

a085731 n = gcd n $ a003415 n -- Reinhard Zumkeller, May 10 2011

(PARI) a(n) = {my(f = factor(n)); for (i=1, #f~, if (f[i, 2] % f[i, 1], f[i, 2]--); ); factorback(f); } \\ Michel Marcus, Feb 14 2016

CROSSREFS

Sequence in context: A234957 A273711 A173675 * A131301 A083730 A008833

Adjacent sequences:  A085728 A085729 A085730 * A085732 A085733 A085734

KEYWORD

nonn,mult

AUTHOR

Reinhard Zumkeller, Jul 20 2003

STATUS

approved

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Last modified June 15 22:19 EDT 2019. Contains 324145 sequences. (Running on oeis4.)