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A323368 Lexicographically earliest sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A003557(i) = A003557(j) and A048250(i) = A048250(j), for all i, j.

%I A323368 #8 Jan 12 2019 20:46:58
%S A323368 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,15,23,24,25,
%T A323368 26,27,28,29,21,30,31,32,31,33,34,35,36,37,38,39,40,41,42,29,31,43,44,
%U A323368 45,46,47,48,49,46,50,51,52,53,54,55,39,56,57,58,59,60,61,62,59,46,63,64,65,66,67,62,68,51,69,70,71,58,72,73,74,75,76,77,78,79,54,80,59,75,81,82,83,84,85,86,87,88,89,90
%N A323368 Lexicographically earliest sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A003557(i) = A003557(j) and A048250(i) = A048250(j), for all i, j.
%C A323368 For all i, j:
%C A323368   a(i) = a(j) => A007814(i) = A007814(j),
%C A323368   a(i) = a(j) => A291751(i) = A291751(j),
%C A323368   a(i) = a(j) => A296089(i) = A296089(j),
%C A323368   a(i) = a(j) => A323238(i) = A323238(j).
%H A323368 Antti Karttunen, <a href="/A323368/b323368.txt">Table of n, a(n) for n = 1..65537</a>
%o A323368 (PARI)
%o A323368 up_to = 65537;
%o A323368 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 A323368 A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
%o A323368 A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
%o A323368 v323368 = rgs_transform(vector(up_to, n, [(n%2), A003557(n), A048250(n)]));
%o A323368 A323368(n) = v323368[n];
%Y A323368 Cf. A000035, A003557, A048250, A291750, A291751, A323238, A323369.
%Y A323368 Differs from A296089 for the first time at n=103, where a(103)=88, while A296089(103)=56.
%Y A323368 Cf. also A323366.
%K A323368 nonn
%O A323368 1,2
%A A323368 _Antti Karttunen_, Jan 12 2019