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).

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, 19, 28, 38, 33, 66, 23, 46, 25, 35, 36, 39, 50, 60, 70, 78, 27, 54, 29, 40, 58, 31, 44, 48, 62, 32, 45, 51, 90, 102, 37, 52, 57, 74, 84, 114, 41, 55, 82, 110, 43, 56, 86

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..16006 (first 10000 rows)

Example

The table begins:
  n   n-th row
  --  --------
   1  1, 2;
   2  3, 6;
   3  4;
   4  5, 10;
   5
   6  7, 12, 14;
   7  8;
   8  9, 15, 18, 30;
   9
  10  11, 22;
  11
  12  13, 20, 21, 26, 42;

Mathematica

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 *)

Crossrefs

The unitary version of A032447.

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

Sequence in context: A178484 A222758 A127915 * A358026 A331117 A282841

Adjacent sequences: A361963 A361964 A361965 * A361967 A361968 A361969

Keyword

nonn,tabf

Author

Amiram Eldar, Apr 01 2023

Status

approved