cp's OEIS Frontend

A300245 Filter sequence combining arithmetic derivative (A003415) with its Möbius transform (A300251).

%I A300245 #11 Mar 24 2018 18:53:41
%S A300245 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 A300245 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 A300245 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 A300245 Filter sequence combining arithmetic derivative (A003415) with its Möbius transform (A300251).
%C A300245 Restricted growth sequence transform of ordered pair [A003415(n), A300251(n)].
%H A300245 Antti Karttunen, <a href="/A300245/b300245.txt">Table of n, a(n) for n = 1..65537</a>
%e A300245 a(16) = a(28) (= 11) because both A003415(16) = A003415(28) = 32 and A300251(16) = A300251(28) = 20.
%o A300245 (PARI)
%o A300245 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 A300245 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A300245 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 A300245 A300251(n) = sumdiv(n,d,moebius(n/d)*A003415(d));
%o A300245 Aux300245(n) = [A003415(n), A300251(n)];
%o A300245 write_to_bfile(1,rgs_transform(vector(65537,n,Aux300245(n))),"b300245.txt");
%Y A300245 Cf. A003415, A300249, A300251, A300252, A300253.
%K A300245 nonn
%O A300245 1,2
%A A300245 _Antti Karttunen_, Mar 08 2018