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A366294 Lexicographically earliest infinite sequence such that a(i) = a(j) => A326042(i) = A326042(j) for all i, j >= 1, where A326042(n) = A064989(sigma(A003961(n))).

%I A366294 #8 Oct 07 2023 21:39:44
%S A366294 1,1,2,3,1,2,2,4,5,1,6,7,8,2,2,9,4,5,2,3,8,6,10,10,11,8,7,7,1,2,12,13,
%T A366294 14,4,2,15,14,2,16,4,17,8,2,13,5,10,16,18,19,11,10,20,10,7,6,10,8,1,5,
%U A366294 7,21,12,22,23,8,14,8,24,25,2,26,27,4,14,28,7,14,16,14,9,29,17,25,20,4,2,2,30,31,5,16,32
%N A366294 Lexicographically earliest infinite sequence such that a(i) = a(j) => A326042(i) = A326042(j) for all i, j >= 1, where A326042(n) = A064989(sigma(A003961(n))).
%C A366294 Restricted growth sequence transform of A326042.
%H A366294 Antti Karttunen, <a href="/A366294/b366294.txt">Table of n, a(n) for n = 1..65537</a>
%o A366294 (PARI)
%o A366294 up_to = 65537;
%o A366294 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 A366294 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A366294 A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
%o A366294 A326042(n) = A064989(sigma(A003961(n)));
%o A366294 v366294  = rgs_transform(vector(up_to,n,A326042(n)));
%o A366294 A366294(n) = v366294[n];
%Y A366294 Cf. A000203, A003961, A064989, A326042.
%Y A366294 Cf. also A286603, A366295.
%K A366294 nonn
%O A366294 1,3
%A A366294 _Antti Karttunen_, Oct 07 2023