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A351236 Lexicographically earliest infinite sequence such that a(i) = a(j) => A344025(i) = A344025(j) and A351085(i) = A351085(j) for all i, j >= 1.

%I A351236 #12 Feb 06 2022 21:24:58
%S A351236 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 A351236 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 A351236 28,40,41,21,2,42,2,43,44,45,46,47,2,48,49,50,2,51,2,52,53,54,46,55,2,56,57,58,2,59,41,60,61,62,2,63,64,65
%N A351236 Lexicographically earliest infinite sequence such that a(i) = a(j) => A344025(i) = A344025(j) and A351085(i) = A351085(j) for all i, j >= 1.
%C A351236 Restricted growth sequence transform of the 4-tuple [A003415(n), A003557(n), A327858(n), A345000(n)].
%C A351236 Question: If an image-analysis algorithm were to classify the scatter plot of this sequence, where it would cluster it? Nearer to A344025 than to A351085?
%H A351236 Antti Karttunen, <a href="/A351236/b351236.txt">Table of n, a(n) for n = 1..65537</a>
%o A351236 (PARI)
%o A351236 up_to = 65537;
%o A351236 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 A351236 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A351236 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A351236 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A351236 A327858(n) = gcd(A003415(n),A276086(n));
%o A351236 A345000(n) = gcd(A003415(n),A003415(A276086(n)));
%o A351236 Aux351236(n) = [A003415(n), A003557(n), A327858(n), A345000(n)];
%o A351236 v351236 = rgs_transform(vector(up_to, n, Aux351236(n)));
%o A351236 A351236(n) = v351236[n];
%Y A351236 Cf. A003415, A003557, A327858, A345000, A351085.
%Y A351236 Differs from A344025 for the first time at n=91, where a(91) = 64, while A344025(91) = 37.
%Y A351236 Cf. also A305800, A351235, A351260.
%K A351236 nonn,easy,look
%O A351236 1,2
%A A351236 _Antti Karttunen_, Feb 06 2022