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A263111 Ordinal transform of the arithmetic derivative A003415.

%I A263111 #6 Dec 11 2023 15:25:19
%S A263111 1,2,1,2,1,3,1,4,1,1,1,5,1,6,1,1,1,7,1,8,1,1,1,9,1,2,1,1,2,10,1,11,1,
%T A263111 1,1,2,1,12,2,2,1,13,1,14,1,1,1,15,1,2,1,1,1,16,1,3,1,1,2,17,2,18,1,1,
%U A263111 1,1,1,19,1,1,1,20,1,21,2,1,2,2,1,22,1,1
%N A263111 Ordinal transform of the arithmetic derivative A003415.
%C A263111 n is the a(n)-th nonnegative integer having its arithmetic derivative.
%H A263111 Alois P. Heinz, <a href="/A263111/b263111.txt">Table of n, a(n) for n = 0..20000</a>
%F A263111 a(n) = |{ j in {0..n} : A003415(j) = A003415(n) }|.
%p A263111 p:= proc() 0 end:
%p A263111 a:= proc(n) option remember; local t;
%p A263111       t:= n*add(i[2]/i[1], i=ifactors(n)[2]);
%p A263111       p(t):= p(t)+1
%p A263111     end:
%p A263111 seq(a(n), n=0..100);
%Y A263111 Cf. A003415.
%K A263111 nonn
%O A263111 0,2
%A A263111 _Alois P. Heinz_, Oct 09 2015