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A351441 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j) and A351450(i) = A351450(j) for all i, j >= 1.

%I A351441 #10 Feb 12 2022 20:30:08
%S A351441 1,1,2,3,1,2,2,4,5,1,6,7,8,2,2,9,10,5,2,3,8,6,11,12,13,8,14,7,1,2,15,
%T A351441 16,17,10,2,18,17,2,19,4,20,8,2,21,5,11,19,22,23,13,11,24,11,14,6,12,
%U A351441 8,1,25,7,26,15,27,28,8,17,8,29,30,2,31,32,10,17,33,7,17,19,17,9,34,20,30,24,10
%N A351441 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j) and A351450(i) = A351450(j) for all i, j >= 1.
%C A351441 Restricted growth sequence transform of the ordered pair [A003557(n), A351450(n)].
%C A351441 For all i, j >= 1:
%C A351441    a(i) = a(j) => A326042(i) = A326042(j),
%C A351441    a(i) = a(j) => A351455(i) = A351455(j).
%H A351441 Antti Karttunen, <a href="/A351441/b351441.txt">Table of n, a(n) for n = 1..65537</a>
%o A351441 (PARI)
%o A351441 up_to = 65537;
%o A351441 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 A351441 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A351441 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A351441 A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
%o A351441 A064989(n) = { my(f = factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
%o A351441 A351450(n) = A064989(A048250(A003961(n)));
%o A351441 Aux351441(n) = [A003557(n), A351450(n)];
%o A351441 v351441 = rgs_transform(vector(up_to, n, Aux351441(n)));
%o A351441 A351441(n) = v351441[n];
%Y A351441 Cf. A003557, A003961, A048250, A064989, A326042, A351450, A351455.
%Y A351441 Cf. also A291751, A351461.
%K A351441 nonn
%O A351441 1,3
%A A351441 _Antti Karttunen_, Feb 12 2022