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A165560 The arithmetic derivative of n, modulo 2. 4
0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Characteristic function of A235991: a(A235991(n))=1 and a(A235992(n))=0. - Reinhard Zumkeller, Mar 11 2014

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for characteristic functions

FORMULA

a(n)= A003415(n) mod 2.

a(n)=(1-(-1)^n’)/2

MAPLE

with(numtheory);

P:=proc(i)

local f, n, p, pfs;

for n from 0 by 1 to i do

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

  print(1/2*(1-(-1)^f));

od;

end:

P(1000);

MATHEMATICA

d[0] = d[1] = 0; d[n_] := n*Total[f = FactorInteger[n]; f[[All, 2]]/f[[All, 1]] ]; a[n_] := Mod[d[n], 2]; Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Apr 22 2015 *)

PROG

(Haskell)

a165560 = flip mod 2 . a003415  -- Reinhard Zumkeller, Mar 11 2014

CROSSREFS

Sequence in context: A286807 A126564 A180433 * A014306 A138150 A271591

Adjacent sequences:  A165557 A165558 A165559 * A165561 A165562 A165563

KEYWORD

easy,nonn

AUTHOR

Paolo P. Lava & Giorgio Balzarotti, Sep 24 2009

EXTENSIONS

Entries checked by R. J. Mathar, Oct 07 2009

STATUS

approved

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Last modified February 16 02:39 EST 2019. Contains 320140 sequences. (Running on oeis4.)