A359419 Nonsquarefree numbers that are both phi-practical and unitary phi-practical.

12, 60, 84, 120, 132, 156, 240, 420, 660, 780, 840, 924, 1020, 1050, 1092, 1140, 1320, 1380, 1428, 1560, 1596, 1680, 1716, 1740, 1860, 1932, 2040, 2100, 2220, 2244, 2280, 2436, 2460, 2508, 2580, 2604, 2640, 2652, 2760, 2820, 2940, 2964, 3036, 3108, 3120, 3180

Offset: 1

Author

Amiram Eldar, Dec 31 2022

Keywords

• nonn

Comments

The squarefree numbers (A005117) are excluded from this sequence since every squarefree phi-practical number is also a unitary phi-practical number.

The least odd term in this sequence is a(104) = 8085.

Links

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

Crossrefs

Intersection of A013929, A260653 and A286906.

Cf. A005117.

Programs

Mathematica

phiPracticalQ[n_] := 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)];
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)]];  (* Frank M Jackson's code at A260653 *)
Select[Range[3200], ! SquareFreeQ[#] && phiPracticalQ[#] && uPhiPracticalQ[#] &]