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A365395 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j) and A365427(i) = A365427(j) for all i, j >= 0.

%I A365395 #10 Sep 04 2023 18:23:39
%S A365395 1,1,1,2,1,3,2,4,1,5,3,6,2,7,4,2,1,8,5,9,3,10,6,3,2,11,7,7,4,12,2,4,1,
%T A365395 13,8,14,5,15,9,5,3,16,10,11,6,17,3,6,2,18,11,10,7,19,7,7,4,17,12,20,
%U A365395 2,7,4,21,1,22,13,23,8,24,14,8,5,25,15,18,9,26,5,9,3,27,16,16,10,28,11,10,6,29,17,30,3,10,6
%N A365395 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j) and A365427(i) = A365427(j) for all i, j >= 0.
%C A365395 Restricted growth sequence transform of the ordered pair [A365425(n), A365427(n)].
%C A365395 Restricted growth sequence transform of the function f(n) = A336390(A163511(n)).
%C A365395 For all i, j: a(i) = a(j) => A365385(i) = A365385(j).
%H A365395 Antti Karttunen, <a href="/A365395/b365395.txt">Table of n, a(n) for n = 0..65537</a>
%F A365395 For all n >= 1, a(n) = a(2*n) = a(A000265(n)).
%o A365395 (PARI)
%o A365395 up_to = 65537;
%o A365395 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 A365395 A000265(n) = (n>>valuation(n,2));
%o A365395 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A365395 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 A365395 A365425(n) = A046523(A000265(A163511(n)));
%o A365395 A336467(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]+1))^f[k,2])); };
%o A365395 A365427(n) = A336467(A163511(n));
%o A365395 A365395aux(n) = [A365425(n), A365427(n)];
%o A365395 v365395 = rgs_transform(vector(1+up_to,n,A365395aux(n-1)));
%o A365395 A365395(n) = v365395[1+n];
%Y A365395 Cf. A000265, A003602, A046523, A163511, A336390, A365385, A365425, A365427, A365394.
%K A365395 nonn
%O A365395 0,4
%A A365395 _Antti Karttunen_, Sep 04 2023