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Lexicographically earliest infinite sequence such that a(i) = a(j) => A366894(i) = A366894(j) for all i, j >= 0.
2

%I #6 Jan 03 2024 17:58:20

%S 1,1,1,1,1,2,1,1,1,3,2,1,1,1,1,1,1,4,3,5,2,1,1,6,1,5,1,1,1,1,1,1,1,7,

%T 4,8,3,5,5,9,2,10,1,11,1,6,6,12,1,1,5,1,1,1,1,1,1,2,1,5,1,1,1,1,1,13,

%U 7,14,4,8,8,15,3,16,5,17,5,9,9,7,2,18,10,19,1,11,11,12,1,20,6,21,6,12,12,7,1,22,1,5,5

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A366894(i) = A366894(j) for all i, j >= 0.

%C Restricted growth sequence transform of A366894.

%C For all i, j >= 0:

%C A366881(i) = A366881(j) => A366806(i) = A366806(j) => a(i) = a(j).

%H Antti Karttunen, <a href="/A366895/b366895.txt">Table of n, a(n) for n = 0..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 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 A336699(n) = A000265(1+A000265(sigma(A000265(n))));

%o A366894(n) = A336699(A163511(n));

%o v366895 = rgs_transform(vector(1+up_to,n,A366894(n-1)));

%o A366895(n) = v366895[1+n];

%Y Cf. A000265, A000593, A163511, A324186, A336699, A351565, A366894.

%Y Cf. also A366806, A366881.

%K nonn

%O 0,6

%A _Antti Karttunen_, Jan 03 2024