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A331297 Lexicographically earliest infinite sequence such that a(i) = a(j) => A263297(i) = A263297(j) and A325225(i) = A325225(j) for all i, j.

%I A331297 #9 Jan 18 2020 18:22:49
%S A331297 1,2,3,3,4,5,6,4,5,7,8,7,9,10,7,6,11,7,12,13,10,14,15,10,7,16,7,17,18,
%T A331297 13,19,8,14,20,10,10,21,22,16,17,23,17,24,25,13,26,27,14,10,13,20,28,
%U A331297 29,10,14,30,22,31,32,17,33,34,17,9,16,25,35,36,26,17,37,14,38,39,13,40,14,28,41,25,10,42,43,30,20,44,31,45,46,17,16,47,34,48,22,16,49,17,25,17
%N A331297 Lexicographically earliest infinite sequence such that a(i) = a(j) => A263297(i) = A263297(j) and A325225(i) = A325225(j) for all i, j.
%C A331297 Restricted growth sequence transform of the unordered pair [A001222(n), A061395(n)].
%H A331297 Antti Karttunen, <a href="/A331297/b331297.txt">Table of n, a(n) for n = 1..65537</a>
%H A331297 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A331297 For all i, j:
%F A331297   A331170(i) = A331170(j) => a(i) = a(j),
%F A331297   A331298(i) = A331298(j) => a(i) = a(j),
%F A331297   A331299(i) = A331299(j) => a(i) = a(j),
%F A331297   a(i) = a(j) => A326846(i) = A326846(j).
%o A331297 (PARI)
%o A331297 up_to = 65537;
%o A331297 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 A331297 A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
%o A331297 Aux331297(n) = { my(a=bigomega(n),b=A061395(n)); [min(a,b),max(a,b)]; };
%o A331297 Aux331297(n) = Set([bigomega(n),A061395(n)]); \\ Alternatively.
%o A331297 v331297 = rgs_transform(vector(up_to, n, Aux331297(n)));
%o A331297 A331297(n) = v331297[n];
%Y A331297 Cf. A001222, A061395, A263297, A325225, A331170, A331298, A331299.
%K A331297 nonn
%O A331297 1,2
%A A331297 _Antti Karttunen_, Jan 18 2020