A365394 - OEIS

%I #14 Oct 26 2023 17:22:26

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

%T 12,7,7,4,13,4,14,3,15,8,16,3,16,9,17,2,13,8,18,5,19,10,20,2,18,10,21,

%U 6,21,11,6,1,22,12,12,7,23,7,24,4,25,13,26,4,26,14,27,3,25,15,28,8,29,16,30,3,28,16,31,9,31,17

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j) and A365426(i) = A365426(j) for all i, j >= 0.

%C Restricted growth sequence transform of the ordered pair [A365425(n), A365426(n)].

%C Restricted growth sequence transform of the function f(n) = A336470(A163511(n)).

%C For all i, j: a(i) = a(j) => A334204(i) = A334204(j).

%H Antti Karttunen, <a href="/A365394/b365394.txt">Table of n, a(n) for n = 0..65537</a>

%F For all n >= 1, a(n) = a(2*n) = a(A000265(n)).

%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 A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));

%o A365425(n) = A046523(A000265(A163511(n)));

%o A336466(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(f[k, 1]-1)^f[k, 2]); };

%o A365426(n) = A336466(A163511(n));

%o A365394aux(n) = [A365425(n), A365426(n)];

%o v365394 = rgs_transform(vector(1+up_to,n,A365394aux(n-1)));

%o A365394(n) = v365394[1+n];

%Y Cf. A000265, A003602, A046523, A163511, A336470, A365425, A365426.

%Y Cf. also A350067, A365395, A366792 (compare the scatter plots).

%K nonn,look

%O 0,4

%A _Antti Karttunen_, Sep 04 2023