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

1,2

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

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[#]  &]

Crossrefs

Intersection of A260653 and A326835.

Cf. A000010.

Sequence in context: A273197 A255427 A181131 * A359418 A354299 A293996

Adjacent sequences: A359414 A359415 A359416 * A359418 A359419 A359420

Keyword

nonn

Author

Amiram Eldar, Dec 31 2022

Status

approved