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A358230 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(i) = A007814(j), A007949(i) = A007949(j) and A046523(i) = A046523(j), for all i, j, where A007814 and A007949 give the 2-adic and 3-adic valuation, and A046523 gives the prime signature of its argument.

%I A358230 #9 Dec 01 2022 22:30:49
%S A358230 1,2,3,4,5,6,5,7,8,9,5,10,5,9,11,12,5,13,5,14,11,9,5,15,16,9,17,14,5,
%T A358230 18,5,19,11,9,20,21,5,9,11,22,5,18,5,14,23,9,5,24,16,25,11,14,5,26,20,
%U A358230 22,11,9,5,27,5,9,23,28,20,18,5,14,11,29,5,30,5,9,31,14,20,18,5,32,33,9,5,27,20,9,11,22,5,34,20,14,11,9,20,35,5,25,23,36,5,18,5,22,37
%N A358230 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(i) = A007814(j), A007949(i) = A007949(j) and A046523(i) = A046523(j), for all i, j, where A007814 and A007949 give the 2-adic and 3-adic valuation, and A046523 gives the prime signature of its argument.
%C A358230 Restricted growth sequence transform of the triple [A007814(n), A007949(n), A046523(n)].
%C A358230 For all i, j:
%C A358230   A305900(i) = A305900(j) => a(i) = a(j),
%C A358230   a(i) = a(j) => A305891(i) = A305891(j),
%C A358230   a(i) = a(j) => A305893(i) = A305893(j),
%C A358230   a(i) = a(j) => A322026(i) = A322026(j) => A072078(i) = A072078(j),
%C A358230   a(i) = a(j) => A065333(i) = A065333(j).
%H A358230 Antti Karttunen, <a href="/A358230/b358230.txt">Table of n, a(n) for n = 1..100000</a>
%o A358230 (PARI)
%o A358230 up_to = 100000;
%o A358230 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 A358230 A007814(n) = valuation(n,2);
%o A358230 A007949(n) = valuation(n,3);
%o A358230 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A358230 v358230 = rgs_transform(vector(up_to, n, [A007814(n), A007949(n), A046523(n)]));
%o A358230 A358230(n) = v358230[n];
%Y A358230 Cf. A007814, A007949, A046523, A065333, A072078, A305891, A305893, A322026.
%Y A358230 Cf. also A358747.
%K A358230 nonn
%O A358230 1,2
%A A358230 _Antti Karttunen_, Dec 01 2022