%I #5 May 28 2019 19:35:05

%S 1,2,3,2,3,4,3,2,5,6,3,7,3,8,9,2,3,10,3,11,12,13,3,14,15,16,17,18,3,

%T 19,3,2,20,21,22,23,3,24,25,26,3,27,3,28,29,30,3,31,32,33,34,35,3,36,

%U 37,38,39,40,3,41,3,42,25,2,43,44,3,45,46,47,3,48,3,49,50,51,52,53,3,54,32,55,3,56,57,58,59,60,3,61,62,63,64,65,66,67,3,68,69,70,3

%N Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) where f(n) = [A034460(n), A325814(n)] for all other numbers, except f(p) = -1 for odd primes.

%C For all i, j:

%C A305801(i) = A305801(j) => a(i) = a(j),

%C A325810(i) = A325810(j) => a(i) = a(j) => A325813(i) = A325813(i).

%H Antti Karttunen, <a href="/A325811/b325811.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o up_to = 65537;

%o 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 A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448

%o A034460(n) = (A034448(n) - n);

%o A048146(n) = (sigma(n)-A034448(n));

%o A325814(n) = (n-A048146(n));

%o Aux325811(n) = if(isprime(n)&&(n%2),-(n%2),[A034460(n), A325814(n)]);

%o v325811 = rgs_transform(vector(up_to,n,Aux325811(n)));

%o A325811(n) = v325811[n];

%Y Cf. A034460, A305801, A325810, A325813, A325814.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 23 2019