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%I #8 Jan 04 2023 01:29:01
%S 1,3,15,105,165,195,255,1155,1785,1995,2145,2415,2805,3045,3135,3255,
%T 3315,3705,3795,3885,4305,4485,4515,4785,4845,4935,5115,5565,5655,
%U 5865,6045,6105,6195,6405,7035,7095,7215,7395,7455,7665,7755,7905,7995,8295,8385,8715
%N Unitary phi-practical (A286906) whose unitary divisors have distinct values of the unitary totient function uphi (A047994).
%C 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.
%C Are all the terms above 3 divisible by 5?
%H Amiram Eldar, <a href="/A359418/b359418.txt">Table of n, a(n) for n = 1..10000</a>
%t uphi[n_] := If[n == 1, 1, (Times @@ (Table[#[[1]]^#[[2]] - 1, {1}] & /@ FactorInteger[n]))[[1]]];
%t 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)]];
%t Select[Range[9000], UnsameQ @@ uphi /@ Divisors[#] && uPhiPracticalQ[#] &]
%Y Intersection of A286906 and A348004.
%Y Cf. A047994, A359417.
%K nonn
%O 1,2
%A _Amiram Eldar_, Dec 31 2022
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