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Irregular table read by rows in which the n-th row consists of all the numbers m such that A323410(m) = n.
4

%I #11 Apr 11 2023 04:18:11

%S 6,10,12,15,14,20,21,18,24,28,35,22,36,40,33,45,26,44,56,39,55,63,52,

%T 72,65,77,34,48,88,51,91,99,38,68,80,104,57,85,117,30,76,112,95,119,

%U 143,46,136,144,69,133,153,50,92,152,176,75,115,171,187,54,100,208

%N Irregular table read by rows in which the n-th row consists of all the numbers m such that A323410(m) = n.

%C The offset is 2 since A323410(p) = 1 for all prime powers p (A246655).

%C The 0th row consists of one term, 1, since 1 is the only solution to A323410(x) = 0.

%H Amiram Eldar, <a href="/A362180/b362180.txt">Table of n, a(n) for n = 2..12684</a> (rows 2..1000)

%e The table begins:

%e n n-th row

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

%e 2

%e 3

%e 4 6;

%e 5

%e 6 10, 12;

%e 7 15;

%e 8 14, 20;

%e 9 21;

%e 10 18, 24, 28;

%e 11 35;

%e 12 22, 36, 40;

%t ucototient[n_] := n - Times @@ (Power @@@ FactorInteger[n] - 1); ucototient[1] = 0;

%t With[{max = 28}, ucot = Table[ucototient[n], {n, 1, max^2}]; row[n_] := Position[ucot, n] // Flatten; Table[row[n], {n, 2, max}] // Flatten]

%Y Cf. A246655, A323410, A362181 (row lengths).

%Y Similar sequences: A032447, A361966, A362213.

%K nonn,tabf

%O 2,1

%A _Amiram Eldar_, Apr 10 2023