%I #11 Mar 24 2018 18:53:41

%S 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,18,19,11,2,

%T 20,2,21,22,23,24,25,2,26,27,28,2,29,2,30,31,32,2,33,34,35,36,37,2,38,

%U 27,39,40,41,2,42,2,43,44,45,46,47,2,48,49,50,2,51,2,52,53,54,46,55,2,56,57,58,2,59,40,60,61,62,2,63,36,64,65,66

%N Filter sequence combining arithmetic derivative (A003415) with its Möbius transform (A300251).

%C Restricted growth sequence transform of ordered pair [A003415(n), A300251(n)].

%H Antti Karttunen, <a href="/A300245/b300245.txt">Table of n, a(n) for n = 1..65537</a>

%e a(16) = a(28) (= 11) because both A003415(16) = A003415(28) = 32 and A300251(16) = A300251(28) = 20.

%o (PARI)

%o rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };

%o write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }

%o A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415

%o A300251(n) = sumdiv(n,d,moebius(n/d)*A003415(d));

%o Aux300245(n) = [A003415(n), A300251(n)];

%o write_to_bfile(1,rgs_transform(vector(65537,n,Aux300245(n))),"b300245.txt");

%Y Cf. A003415, A300249, A300251, A300252, A300253.

%K nonn

%O 1,2

%A _Antti Karttunen_, Mar 08 2018