A335121 Admirable totient numbers: numbers that are equal to the sum of their iterated phi, with one of them taken with a minus sign.

5, 7, 33, 35, 55, 87, 95, 175, 201, 215, 219, 245, 531, 747, 927, 939, 1047, 1295, 1463, 1473, 1551, 1855, 2015, 2103, 2421, 2431, 2547, 2619, 2631, 2765, 3535, 4833, 5067, 5215, 7655, 7743, 7851, 10503, 11127, 11307, 13055, 13707, 16247, 16593, 17805, 18471

Offset

1,1

Comments

Analogous to A111592 (admirable numbers) as A082897 (perfect totient numbers) is analogous to A000396 (perfect numbers).

Links

Amiram Eldar, Table of n, a(n) for n = 1..171 (terms below 10^9)

Example

5 is a term since the values of the iterated phi of 5 are 4, 2 and 1 and 5 = 4 + 2 - 1.

Mathematica

admTotQ[n_] := Module[{s = Most @ Rest @ FixedPointList[EulerPhi, n]}, (ab = Plus @@ s - n) > 0 && EvenQ[ab] && ab/2 < n && MemberQ[s, ab/2]]; Select[Range[8000], admTotQ]

Crossrefs

Subsequence of A286265.

Cf. A000010, A053478, A082897, A111592, A288452.

Sequence in context: A353285 A232237 A104815 * A230997 A243019 A007911

Adjacent sequences: A335118 A335119 A335120 * A335122 A335123 A335124

Keyword

nonn

Author

Amiram Eldar, May 24 2020

Status

approved