A336157 - OEIS

%I #7 Jul 11 2020 17:58:26

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

%T 1,11,6,11,16,2,3,11,17,2,18,2,19,20,7,2,6,4,21,22,23,2,24,22,6,22,17,

%U 2,25,2,26,27,1,11,28,2,6,11,28,2,29,2,5,30,31,11,32,2,31,33,6,2,34,35,3,11,36,2,37,22,38,11,39,40,6,2,41,20,42,2,43,2,44,45

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A318458(i) = A318458(j) and A336158(i) = A336158(j), for all i, j >= 1.

%C Restricted growth sequence transform of the ordered pair [A318458(n), A336158(n)].

%C For all i, j:

%C   A324400(i) = A324400(j) => a(i) = a(j).

%C   A324401(i) = A324401(j) => a(i) = a(j).

%H Antti Karttunen, <a href="/A336157/b336157.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>>valuation(n,2));

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523

%o A336158(n) = A046523(A000265(n));

%o A318458(n) = bitand(n, sigma(n)-n);

%o Aux336157(n) = [A318458(n), A336158(n)];

%o v336157 = rgs_transform(vector(up_to, n, Aux336157(n)));

%o A336157(n) = v336157[n];

%Y Cf. A000265, A046523, A318458, A324400, A324401, A336158.

%Y Cf. A324389, A324530, A324531, A324532 for other similar constructions (also similar by their scatter plots).

%K nonn

%O 1,3

%A _Antti Karttunen_, Jul 11 2020