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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.
11

%I #10 Apr 22 2023 11:38:54

%S 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,

%T 17,27,34,54,19,28,38,56,33,66,23,46,25,35,36,39,50,60,70,72,78,120,

%U 29,58,31,44,48,62,88,96,45,51,90,102,37,52,57,74,84,104,114,168

%N 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.

%H Amiram Eldar, <a href="/A362484/b362484.txt">Table of n, a(n) for n = 1..17858</a> (first 100000 rows)

%e The table begins:

%e n n-th row

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

%e 1 1, 2;

%e 2 3, 6;

%e 3 4, 8;

%e 4 5, 10;

%e 5

%e 6 7, 12, 14, 24;

%e 7

%e 8 9, 15, 18, 30;

%e 9

%e 10 11, 22;

%e 11

%e 12 13, 20, 21, 26, 40, 42;

%t powQ[n_] := n == 2^IntegerExponent[n, 2]; powfQ[n_] := Length[fact = FactorInteger[n]] == 1 && powQ[fact[[1, 2]]];

%t 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};

%t Table[invIPhi[n], {n, 1, 36}] // Flatten (* using the function f by _T. D. Noe_ at A162247 *)

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

%Y Similar sequences: A032447, A361966, A362213, A362180.

%K nonn,tabf

%O 1,2

%A _Amiram Eldar_, Apr 22 2023