A361966 - OEIS

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 #13 Apr 02 2023 08:27:00

%S 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 19,28,38,33,66,23,46,25,35,36,39,50,60,70,78,27,54,29,40,58,31,44,48,

%U 62,32,45,51,90,102,37,52,57,74,84,114,41,55,82,110,43,56,86

%N 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 Amiram Eldar, <a href="/A361966/b361966.txt">Table of n, a(n) for n = 1..16006</a> (first 10000 rows)

%e The table begins:

%e n n-th row

%e -- --------

%e 1 1, 2;

%e 2 3, 6;

%e 3 4;

%e 4 5, 10;

%e 5

%e 6 7, 12, 14;

%e 7 8;

%e 8 9, 15, 18, 30;

%e 9

%e 10 11, 22;

%e 11

%e 12 13, 20, 21, 26, 42;

%t 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 The unitary version of A032447.

%Y Cf. A047994, A135347, A162247, A361967 (row lengths), A361968, A361969, A361970, A361971.

%K nonn,tabf

%O 1,2

%A _Amiram Eldar_, Apr 01 2023