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A361021 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(i) = A007814(j), A001065(i) = A001065(j) and A051953(i) = A051953(j), for all i, j >= 1.

%I A361021 #9 Mar 04 2023 17:07:45
%S A361021 1,2,3,4,3,5,3,6,7,8,3,9,3,10,11,12,3,13,3,14,15,16,3,17,18,19,20,21,
%T A361021 3,22,3,23,24,25,26,27,3,28,29,30,3,31,3,32,33,34,3,35,36,37,38,39,3,
%U A361021 40,29,41,42,43,3,44,3,45,46,47,48,49,3,50,51,52,3,53,3,54,55,56,48,57,3,58,59,60,3,61,42,62,63,64,3,65,38,66,67,68,69,70,3,71
%N A361021 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(i) = A007814(j), A001065(i) = A001065(j) and A051953(i) = A051953(j), for all i, j >= 1.
%C A361021 Restricted growth sequence transform of the triplet [A007814(n), A001065(n), A051953(n)].
%C A361021 For all i, j >= 1:
%C A361021   A305801(i) = A305801(j) => a(i) = a(j),
%C A361021   a(i) = a(j) => A305895(i) = A305895(j),
%C A361021   a(i) = a(j) => A319346(i) = A319346(j).
%H A361021 Antti Karttunen, <a href="/A361021/b361021.txt">Table of n, a(n) for n = 1..100000</a>
%o A361021 (PARI)
%o A361021 up_to = 100000;
%o A361021 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 A361021 A007814(n) = valuation(n,2);
%o A361021 A001065(n) = (sigma(n)-n);
%o A361021 A051953(n) = (n-eulerphi(n));
%o A361021 Aux361021(n) = [A007814(n), A001065(n), A051953(n)];
%o A361021 v361021 = rgs_transform(vector(up_to,n,Aux361021(n)));
%o A361021 A361021(n) = v361021[n];
%Y A361021 Cf. A001065, A007814, A051953.
%Y A361021 Cf. A305801, A305895, A319346.
%Y A361021 Cf. also A353560.
%Y A361021 Differs from A353520 for the first time at n=254, where a(254) = 187, while A353520(254) = 125.
%K A361021 nonn
%O A361021 1,2
%A A361021 _Antti Karttunen_, Mar 03 2023