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%I #11 Jan 04 2023 01:25:50
%S 1,3,15,105,165,195,255,495,525,735,975,1155,1485,1785,1815,1995,2145,
%T 2415,2535,2625,2805,3045,3135,3255,3315,3675,3705,3795,3885,4305,
%U 4455,4485,4515,4785,4845,4875,4935,5115,5145,5445,5565,5655,5865,6045,6105,6195,6405
%N Phi-practical numbers (A260653) whose divisors have distinct values of the Euler totient function (A000010).
%C 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.
%C Are all the terms above 3 divisible by 5?
%H Amiram Eldar, <a href="/A359417/b359417.txt">Table of n, a(n) for n = 1..10000</a>
%t 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 *)
%t Select[Range[40000], UnsameQ @@ EulerPhi[Divisors[#]] && phiPracticalQ[#] &]
%Y Intersection of A260653 and A326835.
%Y Cf. A000010.
%K nonn
%O 1,2
%A _Amiram Eldar_, Dec 31 2022
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