A336927 - OEIS

%I #6 Aug 11 2020 10:38:20

%S 1,2,1,3,2,2,1,4,5,5,2,3,3,2,2,6,5,7,8,9,1,5,2,4,6,9,8,3,4,5,1,10,2,7,

%T 2,10,7,4,3,11,9,2,5,9,7,5,2,6,12,13,5,13,7,4,5,4,8,11,4,9,6,2,5,14,9,

%U 5,15,10,2,5,5,16,11,12,6,7,2,9,8,13,12,10,9,3,7,7,4,11,11,12,3,9,1,5,4,10,13,17,7,18,19,7,5,12,2

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

%C Restricted growth sequence transform of the function f(n) = A335880(A000203(n)), or equally, of the ordered pair [A336928(n), A336929(n)].

%H Antti Karttunen, <a href="/A336927/b336927.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</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 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 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 Aux335880(n) = [A329697(n),A331410(n)];

%o v336927 = rgs_transform(vector(up_to, n, Aux335880(sigma(n))));

%o A336927(n) = v336927[n];

%Y Cf. A000203, A335880, A336928, A336929.

%Y Cf. also A336926.

%K nonn

%O 1,2

%A _Antti Karttunen_, Aug 11 2020