A362484 Irregular table read by rows in which the n-th row consists of all the numbers m such that iphi(m) = n, where iphi is the infinitary totient function A091732.

1, 2, 3, 6, 4, 8, 5, 10, 7, 12, 14, 24, 9, 15, 18, 30, 11, 22, 13, 20, 21, 26, 40, 42, 16, 32, 17, 27, 34, 54, 19, 28, 38, 56, 33, 66, 23, 46, 25, 35, 36, 39, 50, 60, 70, 72, 78, 120, 29, 58, 31, 44, 48, 62, 88, 96, 45, 51, 90, 102, 37, 52, 57, 74, 84, 104, 114, 168

Offset: 1

Author

Amiram Eldar, Apr 22 2023

Keywords

• nonn
• tabf

Examples

			The table begins:
  n   n-th row
  --  -----------------------
   1  1, 2;
   2  3, 6;
   3  4, 8;
   4  5, 10;
   5
   6  7, 12, 14, 24;
   7
   8  9, 15, 18, 30;
   9
  10  11, 22;
  11
  12  13, 20, 21, 26, 40, 42;
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..17858 (first 100000 rows)

Crossrefs

Cf. A091732, A162247, A362485 (row lengths).

Similar sequences: A032447, A361966, A362213, A362180.

Programs

Mathematica

powQ[n_] := n == 2^IntegerExponent[n, 2]; powfQ[n_] := Length[fact = FactorInteger[n]] == 1 && powQ[fact[[1, 2]]];
invIPhi[n_] := Module[{fct = f[n], sol}, sol = Times @@@ (1 + Select[fct, UnsameQ @@ # && AllTrue[# + 1, powfQ] &]); Sort@ Join[sol, 2*sol]]; invIPhi[1] = {1, 2};
Table[invIPhi[n], {n, 1, 36}] // Flatten (* using the function f by T. D. Noe at A162247 *)