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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.

%I A362484 #10 Apr 22 2023 11:38:54
%S A362484 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 A362484 17,27,34,54,19,28,38,56,33,66,23,46,25,35,36,39,50,60,70,72,78,120,
%U A362484 29,58,31,44,48,62,88,96,45,51,90,102,37,52,57,74,84,104,114,168
%N 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.
%H A362484 Amiram Eldar, <a href="/A362484/b362484.txt">Table of n, a(n) for n = 1..17858</a> (first 100000 rows)
%e A362484 The table begins:
%e A362484   n   n-th row
%e A362484   --  -----------------------
%e A362484    1  1, 2;
%e A362484    2  3, 6;
%e A362484    3  4, 8;
%e A362484    4  5, 10;
%e A362484    5
%e A362484    6  7, 12, 14, 24;
%e A362484    7
%e A362484    8  9, 15, 18, 30;
%e A362484    9
%e A362484   10  11, 22;
%e A362484   11
%e A362484   12  13, 20, 21, 26, 40, 42;
%t A362484 powQ[n_] := n == 2^IntegerExponent[n, 2]; powfQ[n_] := Length[fact = FactorInteger[n]] == 1 && powQ[fact[[1, 2]]];
%t A362484 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 A362484 Table[invIPhi[n], {n, 1, 36}] // Flatten (* using the function f by _T. D. Noe_ at A162247 *)
%Y A362484 Cf. A091732, A162247, A362485 (row lengths).
%Y A362484 Similar sequences: A032447, A361966, A362213, A362180.
%K A362484 nonn,tabf
%O A362484 1,2
%A A362484 _Amiram Eldar_, Apr 22 2023