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

Author

Amiram Eldar, May 24 2020

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Subsequence of A286265.

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

Programs

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]