A323157 - OEIS

%I #6 Jan 09 2019 21:22:19

%S 1,2,2,3,2,4,2,5,2,2,2,6,2,7,2,5,2,8,2,9,2,2,2,10,2,2,2,11,2,12,2,13,

%T 2,2,2,14,2,15,2,16,2,17,2,18,2,2,2,19,2,2,2,3,2,20,2,21,2,2,2,22,2,

%U 23,2,13,2,4,2,24,2,7,2,25,2,26,2,27,2,4,2,28,2,2,2,29,2,2,2,30,2,31,2,3,2,2,2,32,2,33,2,9,2,34,2,35,2

%N Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = A000265(A323155(n)) for all n, except with f(1) = 0.

%C For all i, j:

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

%C   A323156(i) = A323156(j) => a(i) = a(j),

%C   a(i) = a(j) => A322977(i) = A322977(j).

%H Antti Karttunen, <a href="/A323157/b323157.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 A000265(n) = (n/2^valuation(n, 2));

%o A323155(n) = { my(m=1); fordiv(n, d, if(isprime(d-1), m *= (d-1)^(1+valuation(n,d-1)))); (m); };

%o A323157aux(n) = if(1==n,0,A000265(A323155(n)));

%o v323157 = rgs_transform(vector(up_to, n, A323157aux(n)));

%o A323157(n) = v323157[n];

%Y Cf. A000265, A305801, A322977, A323155, A323156.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 09 2019