A359418 Unitary phi-practical (A286906) whose unitary divisors have distinct values of the unitary totient function uphi (A047994).

1, 3, 15, 105, 165, 195, 255, 1155, 1785, 1995, 2145, 2415, 2805, 3045, 3135, 3255, 3315, 3705, 3795, 3885, 4305, 4485, 4515, 4785, 4845, 4935, 5115, 5565, 5655, 5865, 6045, 6105, 6195, 6405, 7035, 7095, 7215, 7395, 7455, 7665, 7755, 7905, 7995, 8295, 8385, 8715

Offset

1,2

Comments

A unitary phi-practical number k is a number k such that each number in the range 1..k is a subsum of a the multiset {uphi(d) : d | k, gcd(d, k/d) = 1}. 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

uphi[n_] := If[n == 1, 1, (Times @@ (Table[#[[1]]^#[[2]] - 1, {1}] & /@ FactorInteger[n]))[[1]]];
uDivisors[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &]; uPhiPracticalQ[n_] := If[n < 1, False, If[n == 1, True, (lst = Sort @ Map[uphi, uDivisors[n]]; ok = True; Do[If[lst[[m]] > Sum[lst[[l]], {l, 1, m - 1}] + 1, (ok = False; Break[])], {m, 1, Length[lst]}]; ok)]];
Select[Range[9000], UnsameQ @@ uphi /@ Divisors[#] && uPhiPracticalQ[#] &]

Crossrefs

Intersection of A286906 and A348004.

Cf. A047994, A359417.

Sequence in context: A255427 A181131 A359417 * A354299 A293996 A229726

Adjacent sequences: A359415 A359416 A359417 * A359419 A359420 A359421

Keyword

nonn

Author

Amiram Eldar, Dec 31 2022

Status

approved