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A351460 Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j), A206787(i) = A206787(j) and A336651(i) = A336651(j) for all i, j >= 1.

%I A351460 #15 Feb 14 2022 11:22:17
%S A351460 1,2,3,2,4,3,5,2,6,4,7,3,8,5,9,2,10,6,11,4,12,7,13,3,14,8,15,5,16,9,
%T A351460 17,2,18,10,19,6,20,11,21,4,22,12,23,7,24,13,25,3,26,14,27,8,28,15,29,
%U A351460 5,30,16,31,9,32,17,33,2,34,18,35,10,36,19,37,6,38,20,39,11,40,21,41,4,42,22,43,12,44,23,45,7,46,24,47,13,48,25,49,3,50,26,51,14,52,27,53,8,54
%N A351460 Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j), A206787(i) = A206787(j) and A336651(i) = A336651(j) for all i, j >= 1.
%C A351460 Restricted growth sequence transform of the ordered triplet [A006530(n), A206787(n), A336651(n)].
%C A351460 For all i, j >= 1:
%C A351460   A324400(i) = A324400(j) => a(i) = a(j),
%C A351460   a(i) = a(j) => A347241(i) = A347241(j),
%C A351460   a(i) = a(j) => A351461(i) = A351461(j) => A347240(i) = A347240(j).
%H A351460 Antti Karttunen, <a href="/A351460/b351460.txt">Table of n, a(n) for n = 1..65537</a>
%e A351460 a(429) = a(455) because 429 = 3*11*13 and 455 = 5*7*13, so they have equal largest prime factor (A006530), and they also agree on A206787(429) = A206787(455) = 672 and on A336651(429) = A336651(455) = 1 (because both are squarefree), therefore they get equal value (which is 216) allotted to them by the restricted growth sequence transform. - _Antti Karttunen_, Feb 14 2022
%o A351460 (PARI)
%o A351460 up_to = 65537;
%o A351460 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 A351460 A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
%o A351460 A206787(n) = sumdiv(n, d, d*(d % 2)*issquarefree(d)); \\ From A206787
%o A351460 A336651(n) = { my(f=factor(n)); prod(i=1, #f~, if(2==f[i,1],1,f[i,1]^(f[i,2]-1))); };
%o A351460 Aux351460(n) = [A006530(n), A206787(n), A336651(n)];
%o A351460 v351460 = rgs_transform(vector(up_to, n, Aux351460(n)));
%o A351460 A351460(n) = v351460[n];
%Y A351460 Cf. A006530, A206787, A336651, A347241, A351461.
%Y A351460 Cf. also A324400, A351452.
%Y A351460 Differs from A351454 for the first time at n=121, where a(121) = 62, while A351454(121) = 51.
%Y A351460 Differs from A103391(1+n) for the first time after n=1 at n=455, where a(455) = 216, while A103391(456) = 229.
%K A351460 nonn
%O A351460 1,2
%A A351460 _Antti Karttunen_, Feb 11 2022