Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #8 Dec 31 2018 13:23:01
%S 1,1,1,2,1,2,1,3,3,2,1,3,1,2,3,4,1,5,1,3,3,2,1,4,6,2,7,3,1,5,1,7,3,2,
%T 6,8,1,2,3,4,1,5,1,3,7,2,1,7,8,9,3,3,1,7,6,4,3,2,1,8,1,2,7,7,6,5,1,3,
%U 3,9,1,3,1,2,9,3,8,5,1,7,7,2,1,8,6,2,3,4,1,7,8,3,3,2,6,7,1,10,7,11,1,5,1,4,9
%N Lexicographically earliest such sequence a that a(i) = a(j) => A046523(A322863(i)) = A046523(A322863(j)) for all i, j.
%C Restricted growth sequence transform of A046523(A322863(n)).
%C Equally, restricted growth sequence transform of A278222(A322865(n)).
%C For all i, j: a(i) = a(j) => A322867(i) = A322867(j).
%H Antti Karttunen, <a href="/A322866/b322866.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o (PARI)
%o up_to = 8192;
%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 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 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
%o A322863(n) = if(!n,1,A005940(1+A122111(n)));
%o v322866 = rgs_transform(vector(up_to,n,A046523(A322863(n))));
%o A322866(n) = v322866[n];
%Y Cf. A005940, A046523, A122111, A278222, A286622, A322863, A322865, A322867.
%K nonn
%O 1,4
%A _Antti Karttunen_, Dec 30 2018