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A327970 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(n) = A003415(j) and A327936(i) = A327936(j) for all i, j.

%I A327970 #6 Oct 01 2019 19:52:04
%S A327970 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,14,17,18,11,2,
%T A327970 19,2,20,21,22,23,24,2,12,25,26,2,27,2,28,29,30,2,31,21,32,33,34,2,35,
%U A327970 25,36,37,19,2,36,2,38,39,40,41,42,2,43,44,45,2,46,2,29,47,20,41,48,2,49,50,51,2,52,37,32,53,54,2,55,33,56,57,58,59,60,2,61,62,54,2,63,2,64,48
%N A327970 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(n) = A003415(j) and A327936(i) = A327936(j) for all i, j.
%C A327970 Restricted growth sequence transform of the ordered pair [A003415(n), A327936(n)].
%C A327970 For all i, j:
%C A327970   a(i) = a(j) => A256750(i) = A256750(j),
%C A327970   a(i) = a(j) => A327932(i) = A327932(j).
%H A327970 Antti Karttunen, <a href="/A327970/b327970.txt">Table of n, a(n) for n = 1..65537</a>
%o A327970 (PARI)
%o A327970 up_to = 65537;
%o A327970 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 A327970 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 A327970 A327936(n) = { my(f = factor(n)); for(k=1, #f~, f[k,2] = (f[k,2]>=f[k,1])); factorback(f); };
%o A327970 Aux327970(n) = [A003415(n), A327936(n)];
%o A327970 v327970 = rgs_transform(vector(up_to, n, Aux327970(n)));
%o A327970 A327970(n) = v327970[n];
%Y A327970 Cf. A003415, A256750, A327932, A327936.
%K A327970 nonn
%O A327970 1,2
%A A327970 _Antti Karttunen_, Oct 01 2019