%I #13 Sep 19 2020 16:14:53

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

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

%U 3,8,1,11,1,2,4,6,3,9,1,10,1,2,1,12,6,3,3,6,1,10,11,4,4,2,3,2,1,4,5,5,1,7,1,12,13

%N a(1) = 1 and for n > 1, a(n) = number of values of k, 2 <= k <= n, with A002322(k) = A002322(n), where A002322 is Carmichael lambda.

%C Ordinal transform of f, where f(1) = 0 and f(n) = A002322(n) for n > 1.

%H Antti Karttunen, <a href="/A303758/b303758.txt">Table of n, a(n) for n = 1..65537</a>

%F Except for a(2) = 1, a(n) = A303756(n).

%t a[1] = 1; a[n_] := With[{c = CarmichaelLambda[n]}, Select[Range[2, n], c == CarmichaelLambda[#]&] // Length];

%t Array[a, 1000] (* _Jean-François Alcover_, Sep 19 2020 *)

%o (PARI)

%o up_to = 65537;

%o ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };

%o A002322(n) = lcm(znstar(n)[2]); \\ From A002322

%o Aux303758(n) = if(1==n,0,A002322(n));

%o v303758 = ordinal_transform(vector(up_to,n,Aux303758(n)));

%o A303758(n) = v303758[n];

%Y Cf. A002322.

%Y Cf. also A303756, A303757.

%K nonn

%O 1,4

%A _Antti Karttunen_, Apr 30 2018