A296655 Numbers k such that phi(x) = k has a positive even number of solutions.

1, 4, 6, 10, 12, 16, 18, 22, 24, 28, 30, 36, 42, 46, 52, 54, 58, 64, 66, 70, 78, 80, 82, 84, 88, 100, 102, 106, 110, 112, 126, 130, 136, 138, 148, 150, 160, 162, 166, 168, 172, 176, 178, 180, 184, 190, 196, 198, 200, 208, 210, 222, 224, 226, 228, 232, 238, 250

Offset

1,2

Comments

When the number of solutions is 2, the sum of Sum_{d|x} d*mu(d) is always 0.

A007366 is contained in this sequence because it selects terms with the smallest even number of inverses.

Links

Table of n, a(n) for n=1..58.

Formula

0 = card({phi^-1(a(n))}) mod 2.

Example

1 is a term because phi(1) has two inverses, 1, and 2.
6 is a term because phi(6) has four inverses, 7, 9, 14, and 18.
10 is a term because phi(10) has two inverses, 11, and 22.
18 is a term because phi(18) has four inverses, 19, 27, 38, 54.
348 is a term because phi(348) has six inverses, 349, 413, 531, 698, 826, and 1062.

Mathematica

With[{nn = 1500}, TakeWhile[Union@ Select[KeyValueMap[{#1, Length@ #2} &, PositionIndex@ Array[EulerPhi, nn]], EvenQ@ Last@ # &][[All, 1]], # <= nn/6 &] ] (* Michael De Vlieger, Dec 20 2017 *)

Crossrefs

Cf. A007366, A014197, A032446, A071386.

Sequence in context: A318487 A047233 A194382 * A310577 A353465 A310578

Adjacent sequences: A296652 A296653 A296654 * A296656 A296657 A296658

Keyword

nonn

Author

Torlach Rush, Dec 17 2017

Extensions

Corrected and extended by Rémy Sigrist, Dec 19 2017

Status

approved