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A336460 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A278222(n), A336158(n), A336466(n)], for all i, j >= 1.

%I A336460 #8 Jul 25 2020 10:35:04
%S A336460 1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,3,5,9,3,10,6,11,2,12,7,13,4,14,8,15,
%T A336460 1,16,3,17,5,18,9,19,3,20,10,21,6,22,11,23,2,24,12,25,7,26,13,27,4,28,
%U A336460 14,29,8,30,15,31,1,32,16,33,3,34,17,35,5,18,18,22,9,36,19,37,3,38,20,39,10,40,21,41,6,42,22,43,11,44,23,45,2,7,24,46,12,47,25,48,7,49
%N A336460 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A278222(n), A336158(n), A336466(n)], for all i, j >= 1.
%C A336460 Restricted growth sequence transform of the ordered triple [A278222(n), A336158(n), A336466(n)].
%C A336460 For all i, j:
%C A336460   A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j),
%C A336460   a(i) = a(j) => A336159(i) = A336159(j),
%C A336460   a(i) = a(j) => A336470(i) = A336470(j) => A336471(i) = A336471(j),
%C A336460   a(i) = a(j) => A336472(i) = A336472(j),
%C A336460   a(i) = a(j) => A336473(i) = A336473(j).
%H A336460 Antti Karttunen, <a href="/A336460/b336460.txt">Table of n, a(n) for n = 1..65537</a>
%o A336460 (PARI)
%o A336460 up_to = 65537;
%o A336460 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 A336460 A000265(n) = (n>>valuation(n,2));
%o A336460 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A336460 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A336460 A278222(n) = A046523(A005940(1+n));
%o A336460 A336158(n) = A046523(A000265(n));
%o A336460 A336466(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1))^f[k,2])); };
%o A336460 Aux336460(n) = [A278222(n), A336158(n), A336466(n)];
%o A336460 v336460 = rgs_transform(vector(up_to, n, Aux336460(n)));
%o A336460 A336460(n) = v336460[n];
%Y A336460 Cf. A278222, A336158, A336466.
%Y A336460 Cf. A003602, A324400, A336159, A336470, A336471, A336472, A336473.
%K A336460 nonn
%O A336460 1,3
%A A336460 _Antti Karttunen_, Jul 24 2020