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A351452 Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j) and A278222(i) = A278222(j) for all i, j >= 1.

%I A351452 #11 Feb 11 2022 17:48:49
%S A351452 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 A351452 17,2,18,10,19,6,20,11,21,4,22,12,23,7,24,13,25,3,19,14,26,8,27,15,28,
%U A351452 5,29,16,30,9,31,17,32,2,33,18,34,10,35,19,36,6,37,20,24,11,38,21,39,4,40,22,41,12,42,23,43,7,44,24,45,13,46,25,47,3,48,19,49,14,50,26,51,8,52
%N A351452 Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j) and A278222(i) = A278222(j) for all i, j >= 1.
%C A351452 Restricted growth sequence transform of the ordered pair [A006530(n), A278222(n)].
%C A351452 For all i, j >= 1: A324400(i) = A324400(j) => a(i) = a(j).
%H A351452 Antti Karttunen, <a href="/A351452/b351452.txt">Table of n, a(n) for n = 1..65537</a>
%o A351452 (PARI)
%o A351452 up_to = 65537;
%o A351452 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 A351452 A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
%o A351452 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A351452 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A351452 A278222(n) = A046523(A005940(1+n));
%o A351452 Aux351452(n) = [A006530(n), A278222(n)];
%o A351452 v351452 = rgs_transform(vector(up_to, n, Aux351452(n)));
%o A351452 A351452(n) = v351452[n];
%Y A351452 Cf. A006530, A278222, A286622.
%Y A351452 Cf. also A324400, A336935, A351453, A351454.
%Y A351452 Differs from A351454 and A351460 for the first time at n=49, where a(49) = 19, while A351454(49) = A351460(49) = 26.
%K A351452 nonn
%O A351452 1,2
%A A351452 _Antti Karttunen_, Feb 11 2022