A336159 - OEIS

%I #18 Jul 13 2020 21:32:10

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

%T 13,3,14,5,15,6,16,3,15,8,17,6,18,9,19,2,10,10,20,6,17,11,21,4,16,9,

%U 22,7,19,12,23,1,13,13,6,3,8,14,9,5,15,15,18,6,24,16,19,3,25,15,17,8,26,17,27,6,17,18,28,9,27,19,29,2,6,10,30,10,17,20,22,6,31

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A336158(i) = A336158(j), for all i, j >= 1.

%C Restricted growth sequence transform of the ordered pair [A278222(n), A336158(n)], i.e., of the ordered pair [A046523(A005940(1+n)), A046523(A000265(n))].

%C For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).

%H Antti Karttunen, <a href="/A336159/b336159.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 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

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

%o A278222(n) = A046523(A005940(1+n));

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

%o Aux336159(n) = [A278222(n), A336158(n)];

%o v336159 = rgs_transform(vector(up_to, n, Aux336159(n)));

%o A336159(n) = v336159[n];

%Y Cf. A000265, A005940, A046523, A278222, A336158.

%Y Cf. also A003602, A286163, A286622, A291762, A324400, A336149, A336156, A336157, A336160, A336162.

%K nonn,look

%O 1,3

%A _Antti Karttunen_, Jul 11 2020