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A358747 Lexicographically earliest infinite sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = [A007814(n), A007949(n), A324198(n)] when n > 1, with f(1) = 1.

%I A358747 #11 Dec 02 2022 13:29:40
%S A358747 1,2,3,4,5,6,5,7,8,9,5,10,5,2,11,12,5,13,5,14,3,2,5,15,16,2,17,4,5,6,
%T A358747 5,18,3,2,19,20,5,2,3,21,5,22,5,4,23,2,5,24,19,25,3,4,5,26,27,28,3,2,
%U A358747 5,10,5,2,29,30,5,6,5,4,3,31,5,32,5,2,33,4,19,6,5,34,35,2,5,36,27,2,3,7,5,13,19,4,3,2,5,37,5,38,8,14,5,6,5,7,39
%N A358747 Lexicographically earliest infinite sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = [A007814(n), A007949(n), A324198(n)] when n > 1, with f(1) = 1.
%C A358747 For all i, j: A305900(i) = A305900(j) => a(i) = a(j).
%H A358747 Antti Karttunen, <a href="/A358747/b358747.txt">Table of n, a(n) for n = 1..100000</a>
%o A358747 (PARI)
%o A358747 up_to = 100000;
%o A358747 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 A358747 A007814(n) = valuation(n,2);
%o A358747 A007949(n) = valuation(n,3);
%o A358747 A324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); };
%o A358747 Aux358747(n) = if(1==n,n,[A007814(n), A007949(n), A324198(n)]);
%o A358747 v358747 = rgs_transform(vector(up_to, n,Aux358747(n)));
%o A358747 A358747(n) = v358747[n];
%Y A358747 Cf. A007814, A007949, A324198.
%Y A358747 Cf. also A305900, A358230.
%K A358747 nonn,look
%O A358747 1,2
%A A358747 _Antti Karttunen_, Dec 01 2022