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%I #6 Aug 07 2024 15:11:39
%S 1,2,3,4,2,5,2,6,7,8,2,9,2,10,11,12,2,13,2,14,15,16,2,17,18,19,6,20,2,
%T 21,2,22,23,24,25,26,2,27,16,28,2,29,2,30,9,31,2,32,4,33,19,34,2,35,
%U 36,37,38,39,2,40,2,41,14,42,10,43,2,44,45,46,2,47,2,48,49,50,51,52,2,53,54,55,2,56,57,58,31,59,2,60,8,61,62,63,19,64,2,65,20,66
%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A348717(i) = A348717(j) and A374469(i) = A374469(j), for all i, j >= 1.
%C Restricted growth sequence transform of the ordered pair [A348717(n), A374469(n)].
%H Antti Karttunen, <a href="/A374477/b374477.txt">Table of n, a(n) for n = 1..65537</a>
%o (PARI)
%o up_to = 65537;
%o 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 A348717(n) = if(1==n, 1, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f));
%o A000265(n) = (n>>valuation(n,2));
%o A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A364255(n) = gcd(n, A163511(n));
%o A374469(n) = A000265(A364255(n));
%o Aux374477(n) = [A348717(n), A374469(n)];
%o v374477 = rgs_transform(vector(up_to, n, Aux374477(n)));
%o A374477(n) = v374477[n];
%Y Cf. A163511, A348717, A364255, A374469.
%Y Cf. also A374478.
%K nonn,new
%O 1,2
%A _Antti Karttunen_, Aug 07 2024
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