A335424 - OEIS

%I #7 Jun 13 2020 22:10:04

%S 1,2,2,1,2,3,2,2,1,4,2,2,2,4,3,1,2,2,2,2,4,4,2,3,1,4,2,2,2,5,2,2,4,4,

%T 3,1,2,4,4,4,2,6,2,2,2,4,2,2,1,2,4,2,2,3,4,4,4,4,2,3,2,4,2,1,4,6,2,2,

%U 4,6,2,2,2,4,2,2,3,6,2,2,1,4,2,4,4,4,4,4,2,4,4,2,4,4,4,3,2,2,2,1,2,6,2,4,5

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A335423(i)) = A046523(A335423(j)) for all i, j >= 1.

%C For all i, j: A305800(i) = A305800(j) => a(i) = a(j) => A162642(i) = A162642(j).

%H Antti Karttunen, <a href="/A335424/b335424.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 A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };

%o A248663(n) = A048675(core(n));

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };

%o A335423(n) = A005940(1+A248663(n));

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

%o v335424 = rgs_transform(vector(up_to,n,A046523(A335423(n))));

%o A335424(n) = v335424[n];

%Y Cf. A046523, A162642, A248663, A335423, A335425.

%Y Cf. also A286622, A305800.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 13 2020