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A336162 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A335915(i) = A335915(j), for all i, j >= 1.

%I A336162 #8 Jul 11 2020 17:59:03
%S A336162 1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,9,5,10,3,11,6,12,2,13,7,14,4,15,8,16,
%T A336162 1,17,9,13,5,18,10,19,3,20,11,21,6,22,12,23,2,13,13,24,7,25,14,26,4,
%U A336162 27,15,28,8,29,16,30,1,31,17,32,9,33,13,34,5,35,18,36,10,37,19,38,3,39,20,40,11,41,21,42,6,43,22,44,12,45,23,46,2,47,13,48,13,49,24,50,7,36
%N A336162 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A335915(i) = A335915(j), for all i, j >= 1.
%C A336162 Restricted growth sequence transform of the ordered pair [A278222(n), A335915(n)].
%C A336162 For all i, j: A324400(i) = A324400(j) => a(i) = a(j).
%H A336162 Antti Karttunen, <a href="/A336162/b336162.txt">Table of n, a(n) for n = 1..65537</a>
%o A336162 (PARI)
%o A336162 up_to = 65537;
%o A336162 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 A336162 A000265(n) = (n>>valuation(n,2));
%o A336162 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A336162 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A336162 A278222(n) = A046523(A005940(1+n));
%o A336162 A335915(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1)*A000265(f[k,1]+1))^f[k,2])); };
%o A336162 Aux336162(n) = [A278222(n), A335915(n)];
%o A336162 v336162 = rgs_transform(vector(up_to, n, Aux336162(n)));
%o A336162 A336162(n) = v336162[n];
%Y A336162 Cf. A000265, A005940, A046523, A278222, A335915.
%Y A336162 Cf. also A286622, A324400, A336155, A336159, A336160.
%K A336162 nonn
%O A336162 1,3
%A A336162 _Antti Karttunen_, Jul 11 2020