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A353277 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A020639(n), A341353(n)], with f(1) = 1.

%I A353277 #9 Apr 11 2022 20:48:36
%S A353277 1,2,3,4,5,2,6,2,7,8,9,2,10,2,3,4,11,2,12,2,13,4,14,2,15,2,3,2,16,4,
%T A353277 17,2,3,4,5,18,19,2,7,4,20,2,21,2,3,18,22,2,23,2,3,2,24,2,25,2,7,2,26,
%U A353277 2,27,4,3,8,5,4,28,2,3,2,29,2,30,2,3,2,6,2,31,2,7,4,32,4,15,2,33,18,34,8,35,2,3,8,5,2
%N A353277 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A020639(n), A341353(n)], with f(1) = 1.
%C A353277 Restricted growth sequence transform of function f(1) = 1, and for n > 1, f(n) = [A007814(u), A007949(u)], where u = A156552(n).
%H A353277 Antti Karttunen, <a href="/A353277/b353277.txt">Table of n, a(n) for n = 1..65537</a>
%H A353277 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o A353277 (PARI)
%o A353277 up_to = 65537;
%o A353277 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 A353277 A007814(n) = valuation(n,2);
%o A353277 A007949(n) = valuation(n,3);
%o A353277 A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A353277 Aux353277(n) = if(1==n,1,my(u=A156552(n)); [A007814(u), A007949(u)]);
%o A353277 v353277 = rgs_transform(vector(up_to, n, Aux353277(n)));
%o A353277 A353277(n) = v353277[n];
%Y A353277 Cf. A007814, A007949, A020639, A156552, A341353, A353278 (ordinal transform).
%Y A353277 Cf. also A322026, A340680, A341355.
%K A353277 nonn
%O A353277 1,2
%A A353277 _Antti Karttunen_, Apr 10 2022