A303757 a(1) = 1 and for n > 1, a(n) = number of values of k, 2 <= k <= n, with A000010(k) = A000010(n), where A000010 is Euler totient function phi.

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

Offset

1,4

Comments

Ordinal transform of f, where f(1) = 0 and f(n) = A000010(n) for n > 1.

After a(1)=1 and a(4)=2, the positions of the rest of records is given by A081375(n) = 6, 12, 30, 42, 72, 78, 84, 90, 190, ..., for n >= 3.

Apart from a(2) = 1, the other positions of 1's is given by A210719.

Links

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

Formula

Except for a(2) = 1, a(n) = A081373(n).

Mathematica

With[{s = EulerPhi@ Range@ 105}, MapAt[# + 1 &, Table[Count[s[[2 ;; n]], _?(# == s[[n]] &)], {n, Length@ s}], 1]] (* Michael De Vlieger, Nov 23 2018 *)

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; };
Aux303757(n) = if(1==n, 0, eulerphi(n));
v303757 = ordinal_transform(vector(up_to, n, Aux303757(n)));
A303757(n) = v303757[n];

Crossrefs

Cf. A000010, A081373, A081375, A210719, A303754, A303758, A303777.

Sequence in context: A347042 A333416 A305818 * A182850 A323014 A350331

Adjacent sequences: A303754 A303755 A303756 * A303758 A303759 A303760

Keyword

nonn

Author

Antti Karttunen, Apr 30 2018

Status

approved