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A365384 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351251(i) = A351251(j) for all i, j >= 0, where A351251(n) is the denominator of n / A276086(n).

%I A365384 #10 Sep 07 2023 16:09:53
%S A365384 1,2,3,2,4,5,6,7,8,7,4,9,10,11,12,7,13,14,15,16,12,16,17,18,19,11,20,
%T A365384 21,22,23,24,25,26,25,27,5,28,29,30,29,27,31,10,32,33,29,34,35,36,16,
%U A365384 30,37,38,39,40,37,20,41,42,43,44,45,46,25,47,48,49,50,51,50,27,52,53,54,55,45,56,35,57,58,55,58,59,60,40,58,61,62,63,64,65,45
%N A365384 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351251(i) = A351251(j) for all i, j >= 0, where A351251(n) is the denominator of n / A276086(n).
%C A365384 Restricted growth sequence transform of A351251, or equally, of A351253.
%H A365384 Antti Karttunen, <a href="/A365384/b365384.txt">Table of n, a(n) for n = 0..65537</a>
%o A365384 (PARI)
%o A365384 up_to = 65537;
%o A365384 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 A365384 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A365384 A351251(n) = denominator(n/A276086(n));
%o A365384 v365384 = rgs_transform(vector(1+up_to,n,A351251(n-1)));
%o A365384 A365384(n) = v365384[1+n];
%Y A365384 Cf. A276086, A351251, A351253.
%Y A365384 Cf. also A365393, A365431.
%K A365384 nonn
%O A365384 0,2
%A A365384 _Antti Karttunen_, Sep 07 2023