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A303754 a(1) = 1 and for n > 1, a(n) = number of values of k, 2 <= k <= n, with A303753(k) = A303753(n), where A303753 is ordinal transform of cototient, A051953.

%I A303754 #9 Dec 19 2021 12:39:22
%S A303754 1,1,1,2,1,3,1,2,4,5,1,6,1,3,7,2,1,8,1,4,9,3,1,10,11,12,5,6,1,13,1,4,
%T A303754 14,15,16,17,1,18,19,7,1,20,1,5,21,2,1,22,8,9,23,24,1,25,10,11,12,6,1,
%U A303754 26,1,7,27,3,28,29,1,13,30,14,1,31,1,32,33,34,15,35,1,16,17,36,1,37,8,18,38,9,1,39,19,4,40,2,41,42,1,43,44,20,1,45,1,21
%N A303754 a(1) = 1 and for n > 1, a(n) = number of values of k, 2 <= k <= n, with A303753(k) = A303753(n), where A303753 is ordinal transform of cototient, A051953.
%C A303754 Ordinal transform of f, where f(1) = 0 and f(n) = A303753(n) for n > 1.
%H A303754 Antti Karttunen, <a href="/A303754/b303754.txt">Table of n, a(n) for n = 1..65537</a>
%t A303754 b[_] = 0;
%t A303754 A303753[n_] := A303753[n] = With[{t = EulerPhi[n] - n}, b[t] = b[t]+1];
%t A303754 f[n_] := If[n == 1, 0, A303753[n]];
%t A303754 Clear[b]; b[_] = 0;
%t A303754 a[n_] := a[n] = With[{t = f[n]}, b[t] = b[t]+1];
%t A303754 Array[a, 105] (* _Jean-François Alcover_, Dec 19 2021 *)
%o A303754 (PARI)
%o A303754 up_to = 65537;
%o A303754 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 A303754 A051953(n) = (n - eulerphi(n));
%o A303754 v303753 = ordinal_transform(vector(up_to,n,A051953(n)));
%o A303754 Aux303754(n) = if(1==n,0,v303753[n]);
%o A303754 v303754 = ordinal_transform(vector(up_to,n,Aux303754(n)));
%o A303754 A303754(n) = v303754[n];
%Y A303754 Cf. A051953, A303753.
%Y A303754 Cf. also A081373, A303757.
%K A303754 nonn
%O A303754 1,4
%A A303754 _Antti Karttunen_, Apr 30 2018