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First differences of the arithmetic derivative sequence A003415.
3

%I #20 Jun 10 2015 06:44:31

%S 0,1,0,3,-3,4,-4,11,-6,1,-6,15,-15,8,-1,24,-31,20,-20,23,-14,3,-12,43,

%T -34,5,12,5,-31,30,-30,79,-66,5,-7,48,-59,20,-5,52,-67,40,-40,47,-9,

%U -14,-24,111,-98,31,-25,36,-55,80,-65,76,-70,9,-30,91,-91,32,18

%N First differences of the arithmetic derivative sequence A003415.

%C |a(A258765(n))| = n and |a(m)| != n for m < A258765(n). - _Reinhard Zumkeller_, Jun 10 2015

%H Alois P. Heinz, <a href="/A258057/b258057.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A003415(n+1) - A003415(n).

%p d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):

%p a:= n-> d(n+1)-d(n):

%p seq(a(n), n=0..105);

%o (Haskell)

%o a258057 n = a258057_list !! n

%o a258057_list = zipWith (-) (tail a003415_list) a003415_list

%o -- _Reinhard Zumkeller_, Jun 10 2015

%Y Cf. A003415.

%Y Cf. A258765.

%K sign,look

%O 0,4

%A _Alois P. Heinz_, Jun 08 2015