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A351235 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j), A327858(i) = A327858(j) and A345000(i) = A345000(j) for all i, j >= 1.

%I A351235 #11 Feb 06 2022 21:24:38
%S A351235 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,7,2,15,16,17,18,8,2,
%T A351235 19,2,20,21,7,22,23,2,24,10,25,2,19,2,26,27,28,2,29,30,31,14,32,2,33,
%U A351235 10,25,10,7,2,34,2,9,27,35,36,19,2,13,10,19,2,37,2,9,38,39,36,19,2,40,41,7,2,34,10,17,10,42,2
%N A351235 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j), A327858(i) = A327858(j) and A345000(i) = A345000(j) for all i, j >= 1.
%C A351235 Restricted growth sequence transform of the triplet [A046523(n), A327858(n), A345000(n)].
%C A351235 For all i, j >= 1:
%C A351235   A305800(i) = A305800(j) => a(i) = a(j) => A351085(i) = A351085(j).
%H A351235 Antti Karttunen, <a href="/A351235/b351235.txt">Table of n, a(n) for n = 1..65537</a>
%o A351235 (PARI)
%o A351235 up_to = 65537;
%o A351235 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 A351235 A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
%o A351235 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A351235 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A351235 A327858(n) = gcd(A003415(n),A276086(n));
%o A351235 A345000(n) = gcd(A003415(n),A003415(A276086(n)));
%o A351235 Aux351235(n) = [A046523(n), A327858(n), A345000(n)];
%o A351235 v351235 = rgs_transform(vector(up_to,n,Aux351235(n)));
%o A351235 A351235(n) = v351235[n];
%Y A351235 Cf. A003415, A046523, A276086, A327858, A345000, A351086.
%Y A351235 Cf. also A101296, A305800, A329620, A351085, A351236.
%K A351235 nonn,easy
%O A351235 1,2
%A A351235 _Antti Karttunen_, Feb 06 2022