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 A359418 Unitary phi-practical (A286906) whose unitary divisors have distinct values of the unitary totient function uphi (A047994). 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 10 12:17 EDT 2023. Contains 363205 sequences. (Running on oeis4.)