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A361966 Irregular table read by rows in which the n-th row consists of all the numbers m such that uphi(m) = n, where uphi is the unitary totient function (A047994).

%I A361966 #13 Apr 02 2023 08:27:00
%S A361966 1,2,3,6,4,5,10,7,12,14,8,9,15,18,30,11,22,13,20,21,26,42,24,16,17,34,
%T A361966 19,28,38,33,66,23,46,25,35,36,39,50,60,70,78,27,54,29,40,58,31,44,48,
%U A361966 62,32,45,51,90,102,37,52,57,74,84,114,41,55,82,110,43,56,86
%N A361966 Irregular table read by rows in which the n-th row consists of all the numbers m such that uphi(m) = n, where uphi is the unitary totient function (A047994).
%H A361966 Amiram Eldar, <a href="/A361966/b361966.txt">Table of n, a(n) for n = 1..16006</a> (first 10000 rows)
%e A361966 The table begins:
%e A361966   n   n-th row
%e A361966   --  --------
%e A361966    1  1, 2;
%e A361966    2  3, 6;
%e A361966    3  4;
%e A361966    4  5, 10;
%e A361966    5
%e A361966    6  7, 12, 14;
%e A361966    7  8;
%e A361966    8  9, 15, 18, 30;
%e A361966    9
%e A361966   10  11, 22;
%e A361966   11
%e A361966   12  13, 20, 21, 26, 42;
%t A361966 invUPhi[n_] := Module[{fct = f[n], sol}, sol = Times @@@ (1 + Select[fct, UnsameQ @@ # && (Length[#] == 1 || CoprimeQ @@ (# + 1)) && Times @@ PrimeNu[# + 1] == 1 &]); Sort@ Join[sol, 2*Select[sol, OddQ]]]; invUPhi[1] = {1, 2}; Table[invUPhi[n], {n, 1, 50}] // Flatten (* using the function f by _T. D. Noe_ at A162247 *)
%Y A361966 The unitary version of A032447.
%Y A361966 Cf. A047994, A135347, A162247, A361967 (row lengths), A361968, A361969, A361970, A361971.
%K A361966 nonn,tabf
%O A361966 1,2
%A A361966 _Amiram Eldar_, Apr 01 2023