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A336926 Lexicographically earliest infinite sequence such that a(i) = a(j) => A335880(1+sigma(i)) = A335880(1+sigma(j)), for all i, j >= 1.

%I A336926 #7 Aug 10 2020 22:19:29
%S A336926 1,1,2,1,3,4,4,1,3,5,4,6,7,8,8,1,5,2,9,10,5,6,8,9,1,10,7,11,12,13,5,1,
%T A336926 14,6,14,9,5,9,11,10,10,7,6,15,10,13,14,16,6,14,13,11,6,11,13,11,11,
%U A336926 10,9,11,10,7,11,1,15,17,10,18,7,17,13,14,13,11,16,19,7,11,11,13,9,18,15,17,20,21,11,11,10,21,13,11,21,17,11,21,11,10,11,20,5
%N A336926 Lexicographically earliest infinite sequence such that a(i) = a(j) => A335880(1+sigma(i)) = A335880(1+sigma(j)), for all i, j >= 1.
%C A336926 Restricted growth sequence transform of the function f(n) = A335880(A088580(n)).
%C A336926 For all i, j:
%C A336926   A324400(i) = A324400(j) => a(i) = a(j),
%C A336926   a(i) = a(j) => A336694(i) = A336694(j),
%C A336926   a(i) = a(j) => A336695(i) = A336695(j).
%H A336926 Antti Karttunen, <a href="/A336926/b336926.txt">Table of n, a(n) for n = 1..65537</a>
%H A336926 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A336926 (PARI)
%o A336926 up_to = 65537;
%o A336926 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 A336926 A329697(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A329697(f[k,1]-1)))); };
%o A336926 A331410(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A331410(f[k,1]+1)))); };
%o A336926 Aux335880(n) = [A329697(n),A331410(n)];
%o A336926 v336926 = rgs_transform(vector(up_to, n, Aux335880(1+sigma(n))));
%o A336926 A336926(n) = v336926[n];
%Y A336926 Cf. A000203, A088580, A329697, A331410, A332459, A335880, A336694, A336695.
%Y A336926 Cf. also A336925.
%K A336926 nonn
%O A336926 1,3
%A A336926 _Antti Karttunen_, Aug 10 2020