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

1,4

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

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 *)

Prog

(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];

Crossrefs

Cf. A051953, A303753.

Cf. also A081373, A303757.

Sequence in context: A270656 A380495 A045898 * A380508 A257918 A257912

Adjacent sequences: A303751 A303752 A303753 * A303755 A303756 A303757

Keyword

nonn

Author

Antti Karttunen, Apr 30 2018

Status

approved