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.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Apr 30 2018

Keywords

• nonn

Comments

Ordinal transform of f, where f(1) = 0 and f(n) = A303753(n) for n > 1.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A051953, A303753.

Cf. also A081373, A303757.

Programs

Mathematica

b[_] = 0;
A303753[n_] := A303753[n] = With[{t = EulerPhi[n] - n}, b[t] = b[t]+1];
f[n_] := If[n == 1, 0, A303753[n]];
Clear[b]; b[_] = 0;
a[n_] := a[n] = With[{t = f[n]}, b[t] = b[t]+1];
Array[a, 105] (* Jean-François Alcover, Dec 19 2021 *)

PARI

up_to = 65537;
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; };
A051953(n) = (n - eulerphi(n));
v303753 = ordinal_transform(vector(up_to,n,A051953(n)));
Aux303754(n) = if(1==n,0,v303753[n]);
v303754 = ordinal_transform(vector(up_to,n,Aux303754(n)));
A303754(n) = v303754[n];