A336151 - OEIS

%I #7 Jul 11 2020 17:57:40

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

%T 17,18,2,13,19,10,5,20,21,15,7,22,23,24,13,7,25,26,5,6,7,19,15,27,5,

%U 13,10,21,28,29,17,30,31,10,2,15,32,33,19,25,23,34,5,35,36,7,21,13,37,38,7,3,39,40,23,19,41,28,13,42,17,15,25,31,43,21,5,44,10,13,7,45,46,47,15,23

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A001221(i) = A001221(j) and A006530(i) = A006530(j), for all i, j >= 1.

%C Restricted growth sequence transform of the ordered pair [A001221(n), A006530(n)]. The first member of pair gives the number of distinct prime divisors of n, and the second member gives its largest prime factor.

%C For all i, j: A324400(i) = A324400(j) => A286621(i) = A286621(j) => a(i) = a(j).

%H Antti Karttunen, <a href="/A336151/b336151.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 A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);

%o Aux336151(n) = [omega(n), A006530(n)];

%o v336151 = rgs_transform(vector(up_to, n, Aux336151(n)));

%o A336151(n) = v336151[n];

%Y Cf. A001221, A006530.

%Y Cf. also A286621, A324400, A336150, A336152.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 11 2020