A318835 - OEIS

%I #6 Sep 05 2018 06:13:20

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

%T 17,2,18,19,20,21,22,2,23,24,25,2,26,2,27,28,29,2,30,9,31,32,33,2,34,

%U 24,35,36,37,2,38,2,39,40,39,41,42,2,43,44,45,2,46,2,47,48,49,50,51,2,52,53,54,2,55,56,57,58,59,2,60,61,62,63,64,65,66,2

%N Restricted growth sequence transform of A318834, product_{d|n, d<n} A019565(A000010(d)).

%C For all i, j: a(i) = a(j) => A051953(i) = A051953(j).

%H Antti Karttunen, <a href="/A318835/b318835.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 A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565

%o A318834(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A019565(eulerphi(d)))); m; };

%o v318835 = rgs_transform(vector(up_to,n,A318834(n)));

%o A318835(n) = v318835[n];

%Y Cf. A000010, A019565, A318831, A318834,

%Y Cf. also A293215, A293217, A293223, A293224, A293232, A300833, A300835.

%K nonn

%O 1,2

%A _Antti Karttunen_, Sep 04 2018