This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A212663 #6 May 24 2012 16:04:32 %S A212663 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 A212663 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 A212663 1,0,0,1,0,0,2,0,0,2,0,0,1,1,0,1,2,0,1 %N A212663 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 A212663 Paolo P. Lava, <a href="/A212663/b212663.txt">Table of n, a(n) for n = 1..5000</a> %p A212663 with(numtheory); %p A212663 A212663:=proc(q) %p A212663 local a,b,c,i,n,p,pfs,t; %p A212663 for n from 1 to q do %p A212663 pfs:=ifactors(n)[2]; a:=n*add(op(2,p)/op(1,p),p=pfs); t:=0; %p A212663 for i from 1 to trunc(n/2) do %p A212663 pfs:=ifactors(i)[2]; b:=i*add(op(2,p)/op(1,p),p=pfs); %p A212663 pfs:=ifactors(n-i)[2]; c:=(n-i)*add(op(2,p)/op(1,p),p=pfs); %p A212663 if a=b+c then t:=t+1; fi; %p A212663 od; %p A212663 print(t); %p A212663 od; end: %p A212663 A212663(1000); %Y A212663 Cf. A003415, A211223-A211225, A212662, A212664. %K A212663 nonn %O A212663 1,39 %A A212663 _Paolo P. Lava_, May 23 2012