cp's OEIS Frontend

A347374 Lexicographically earliest infinite sequence such that a(i) = a(j) => A331410(i) = A331410(j) and A000593(i) = A000593(j), for all i, j >= 1.

%I A347374 #9 Jan 30 2022 09:51:38
%S A347374 1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,9,5,10,3,11,6,12,2,13,7,14,4,15,8,16,
%T A347374 1,17,9,17,5,18,10,19,3,20,11,21,6,22,12,23,2,24,13,25,7,26,14,25,4,
%U A347374 27,15,28,8,29,16,30,1,31,17,32,9,33,17,34,5,35,18,36,10,33,19,37,3,38,20,39,11,40,21,41,6,42,22,43,12
%N A347374 Lexicographically earliest infinite sequence such that a(i) = a(j) => A331410(i) = A331410(j) and A000593(i) = A000593(j), for all i, j >= 1.
%C A347374 Restricted growth sequence transform of the ordered pair [A000593(n), A331410(n)].
%C A347374 For all i, j: A003602(i) = A003602(j) => a(i) = a(j) => A347249(i) = A347249(j).
%H A347374 Antti Karttunen, <a href="/A347374/b347374.txt">Table of n, a(n) for n = 1..65537</a>
%o A347374 (PARI)
%o A347374 up_to = 65537;
%o A347374 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 A347374 A000593(n) = sigma(n>>valuation(n, 2));
%o A347374 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 A347374 Aux347374(n) = [A331410(n), A000593(n)];
%o A347374 v347374 = rgs_transform(vector(up_to, n, Aux347374(n)));
%o A347374 A347374(n) = v347374[n];
%Y A347374 Cf. A000593, A003602, A331410, A347249.
%Y A347374 Cf. also A335880, A336390, A336391, A336394 for similar constructions.
%K A347374 nonn
%O A347374 1,3
%A A347374 _Antti Karttunen_, Aug 29 2021