A359417 Phi-practical numbers (A260653) whose divisors have distinct values of the Euler totient function (A000010).

1, 3, 15, 105, 165, 195, 255, 495, 525, 735, 975, 1155, 1485, 1785, 1815, 1995, 2145, 2415, 2535, 2625, 2805, 3045, 3135, 3255, 3315, 3675, 3705, 3795, 3885, 4305, 4455, 4485, 4515, 4785, 4845, 4875, 4935, 5115, 5145, 5445, 5565, 5655, 5865, 6045, 6105, 6195, 6405

Offset: 1

Author

Amiram Eldar, Dec 31 2022

Keywords

• nonn

Comments

A phi-practical number k is a number k such that each number in the range 1..k is a subsum of a the multiset {phi(d) : d | k}. This sequence is restricted to cases in which all the values in this multiset are distinct.

Are all the terms above 3 divisible by 5?

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A260653 and A326835.

Cf. A000010.

Programs

Mathematica

phiPracticalQ[n_] := If[n<1, False, If[n==1, True, (lst = Sort @ EulerPhi @ Divisors[n]; ok = True; Do[If[lst[[m]]>Sum[lst[[l]], {l, 1, m-1}]+1, (ok=False; Break[])], {m, 1, Length[lst]}]; ok)]]; (* Frank M Jackson's code at A260653 *)
Select[Range[40000], UnsameQ @@ EulerPhi[Divisors[#]] && phiPracticalQ[#]  &]