%I #12 Jun 12 2018 10:17:05

%S 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,15,10,18,2,

%T 19,2,20,21,7,22,23,2,15,21,24,2,25,2,26,27,28,2,29,30,31,10,26,2,32,

%U 33,34,21,28,2,35,2,36,37,38,33,39,2,13,40,41,2,42,2,43,44,26,45,46,2,47,48,43,2,49,50,51,40,52,2,53,45,54,55,56,33,57,2,58,59

%N Restricted growth sequence transform of A305792, a filter sequence constructed from binary expansions of the proper divisors of n.

%H Antti Karttunen, <a href="/A305793/b305793.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>

%F For all i, j:

%F a(i) = a(j) => A000005(i) = A000005(j).

%F a(i) = a(j) => A292257(i) = A292257(j).

%F a(i) = a(j) => A305426(i) = A305426(j).

%F a(i) = a(j) => A305435(i) = A305435(j).

%o (PARI)

%o \\ Needs also code from A286622:

%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 A305792(n) = { my(m=1); fordiv(n,d,if(d<n, m *= prime(A286622(d)-1))); (m); };

%o v305793 = rgs_transform(vector(up_to, n, A305792(n)));

%o A305793(n) = v305793[n];

%Y Cf. A278222, A286622, A305792, A305795.

%Y Cf. also A293215, A300833, A304103, A305813.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 11 2018