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A353560 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j), A001065(i) = A001065(j) and A051953(i) = A051953(j), for all i, j >= 1.

%I A353560 #8 Apr 29 2022 15:55:35
%S A353560 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,18,19,20,2,
%T A353560 21,2,22,23,24,25,26,2,27,28,29,2,30,2,31,32,33,2,34,35,36,37,38,2,39,
%U A353560 28,40,41,42,2,43,2,44,45,46,47,48,2,49,50,51,2,52,2,53,54,55,47,56,2,57,58,59,2,60,41,61,62,63,2,64,37
%N A353560 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j), A001065(i) = A001065(j) and A051953(i) = A051953(j), for all i, j >= 1.
%C A353560 Restricted growth sequence transform of the triplet [A046523(n), A001065(n), A051953(n)].
%C A353560 For all i,j:
%C A353560   A305800(i) = A305800(j) => a(i) = a(j),
%C A353560   a(i) = a(j) => A300232(i) = A300232(j), [Combining A046523 and A051953]
%C A353560   a(i) = a(j) => A300235(i) = A300235(j), [Combining A046523 and A001065]
%C A353560   a(i) = a(j) => A305895(i) = A305895(j), [Combining A001065 and A051953]
%C A353560   a(i) = a(j) => A353276(i) = A353276(j). [Needs all three components]
%H A353560 Antti Karttunen, <a href="/A353560/b353560.txt">Table of n, a(n) for n = 1..100000</a>
%o A353560 (PARI)
%o A353560 up_to = 100000;
%o A353560 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 A353560 A001065(n) = (sigma(n)-n);
%o A353560 A051953(n) = (n-eulerphi(n));
%o A353560 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A353560 Aux353560(n) = [A046523(n), A001065(n), A051953(n)];
%o A353560 v353560 = rgs_transform(vector(up_to,n,Aux353560(n)));
%o A353560 A353560(n) = v353560[n];
%Y A353560 Cf. A001065, A046523, A051953.
%Y A353560 Cf. also A101296, A305800, A300232, A353276.
%Y A353560 Differs from A300235 for the first time at n=153, where a(153) = 110, while A300235(153) = 106.
%Y A353560 Differs from A305895 for the first time at n=3283, where a(3283) = 2502, while A305895(3283) = 1845.
%Y A353560 Differs from A327931 for the first time at n=4433, where a(4433) = 2950, while A327931(4433) = 3393.
%Y A353560 Differs from A300249 and from A351260 for the first time at n=105, where a(105) = 75, while A300249(105) = A351260(105) = 56.
%K A353560 nonn
%O A353560 1,2
%A A353560 _Antti Karttunen_, Apr 29 2022