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A351037 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000593(i) = A000593(j), for all i, j >= 1, where A000593 is the sum of odd divisors function.

%I A351037 #15 Feb 01 2022 18:57:14
%S A351037 1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,9,5,10,3,11,6,8,2,12,7,13,4,14,8,11,
%T A351037 1,15,9,15,5,16,10,17,3,18,11,19,6,20,8,15,2,21,12,22,7,23,13,22,4,24,
%U A351037 14,25,8,26,11,27,1,28,15,29,9,30,15,22,5,31,16,32,10,30,17,24,3,33,18,28,11,34,19,35,6,36
%N A351037 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000593(i) = A000593(j), for all i, j >= 1, where A000593 is the sum of odd divisors function.
%C A351037 Restricted growth sequence transform of A000593.
%C A351037 Question: To which set of n does the horizontal stripe at around a(n) = ~8000 correspond in the scatter plot of this sequence?
%H A351037 Antti Karttunen, <a href="/A351037/b351037.txt">Table of n, a(n) for n = 1..65537</a>
%e A351037 a(21) = a(31) = 11 because A000593(21) = A000593(31) = 32, and 32 is the 11th distinct value obtained by A000593.
%o A351037 (PARI)
%o A351037 up_to = 65537;
%o A351037 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 A351037 v351037 = rgs_transform(vector(up_to, n, sigma(n>>valuation(n,2))));
%o A351037 A351037(n) = v351037[n];
%Y A351037 Cf. A000593.
%Y A351037 Cf. also A286603, A347374, A351036, A351040, A351090.
%K A351037 nonn,easy,look
%O A351037 1,3
%A A351037 _Antti Karttunen_, Jan 31 2022