%I #6 May 24 2012 16:04:32

%S 0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,0,

%T 0,1,0,0,2,0,0,1,0,0,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,

%U 1,0,0,1,0,0,2,0,0,2,0,0,1,1,0,1,2,0,1

%N Number of ways to represent n’ as x’ + y’, where x+y = n, x > 0, and n’, x’, y’ are the arithmetic derivatives of n, x, y.

%H Paolo P. Lava, <a href="/A212663/b212663.txt">Table of n, a(n) for n = 1..5000</a>

%p with(numtheory);

%p A212663:=proc(q)

%p local a,b,c,i,n,p,pfs,t;

%p for n from 1 to q do

%p pfs:=ifactors(n)[2]; a:=n*add(op(2,p)/op(1,p),p=pfs); t:=0;

%p for i from 1 to trunc(n/2) do

%p pfs:=ifactors(i)[2]; b:=i*add(op(2,p)/op(1,p),p=pfs);

%p pfs:=ifactors(n-i)[2]; c:=(n-i)*add(op(2,p)/op(1,p),p=pfs);

%p if a=b+c then t:=t+1; fi;

%p od;

%p print(t);

%p od; end:

%p A212663(1000);

%Y Cf. A003415, A211223-A211225, A212662, A212664.

%K nonn

%O 1,39

%A _Paolo P. Lava_, May 23 2012