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

1,2

Links

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

Example

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;

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 *)

Crossrefs

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

Similar sequences: A032447, A361966, A362213, A362180.

Sequence in context: A291604 A082332 A154285 * A258078 A036552 A257987

Adjacent sequences: A362481 A362482 A362483 * A362485 A362486 A362487

Keyword

nonn,tabf

Author

Amiram Eldar, Apr 22 2023

Status

approved