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A351949 Lexicographically earliest infinite sequence such that a(i) = a(j) => A246277(A329044(i)) = A246277(A329044(j)) and A003557(i) = A003557(j), for all i, j >= 1.

%I A351949 #8 Apr 06 2022 18:14:53
%S A351949 1,2,2,3,2,4,2,5,6,4,2,7,2,4,8,9,2,10,2,7,8,4,2,11,12,4,13,7,2,14,2,
%T A351949 15,8,4,16,17,2,4,8,5,2,18,2,7,19,4,2,20,21,22,8,7,2,23,24,25,8,4,2,
%U A351949 26,2,4,27,28,29,30,2,7,8,31,2,32,2,4,33,7,34,30,2,9,35,4,2,36,37,4,8,25,2,38,39,7,8,4,40
%N A351949 Lexicographically earliest infinite sequence such that a(i) = a(j) => A246277(A329044(i)) = A246277(A329044(j)) and A003557(i) = A003557(j), for all i, j >= 1.
%C A351949 Restricted growth sequence transform of the ordered pair [A003557(n), A329345(n)].
%H A351949 Antti Karttunen, <a href="/A351949/b351949.txt">Table of n, a(n) for n = 1..65537</a>
%o A351949 (PARI)
%o A351949 up_to = 65537;
%o A351949 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 A351949 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A351949 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A351949 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };
%o A351949 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A351949 A324886(n) = A276086(A108951(n));
%o A351949 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A351949 A329044(n) = A064989(A324886(n));
%o A351949 A246277(n) = if(1==n, 0, 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)/2);
%o A351949 v351949 = rgs_transform(vector(up_to, n, [A003557(n), A246277(A329044(n))]));
%o A351949 A351949(n) = v351949[n];
%Y A351949 Cf. A003557, A305800, A329044, A329345, A329620.
%K A351949 nonn
%O A351949 1,2
%A A351949 _Antti Karttunen_, Apr 05 2022