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A378638 Irregular triangle read by rows: row n lists all m such that phi(m) divides n, where phi is the Euler totient function (A000010).

%I A378638 #32 Dec 06 2024 11:31:29
%S A378638 1,2,1,2,3,4,6,1,2,1,2,3,4,5,6,8,10,12,1,2,1,2,3,4,6,7,9,14,18,1,2,1,
%T A378638 2,3,4,5,6,8,10,12,15,16,20,24,30,1,2,1,2,3,4,6,11,22,1,2,1,2,3,4,5,6,
%U A378638 7,8,9,10,12,13,14,18,21,26,28,36,42,1,2,1,2,3,4,6,1,2
%N A378638 Irregular triangle read by rows: row n lists all m such that phi(m) divides n, where phi is the Euler totient function (A000010).
%C A378638 If n is odd, row n is {1, 2}.
%C A378638 If n is even, row n begins with {1, 2, 3, 4}.
%H A378638 Paolo Xausa, <a href="/A378638/b378638.txt">Table of n, a(n) for n = 1..13988</a> (rows 1..1000 of triangle, flattened).
%F A378638 T(n,k) <= n^2, for n > 2 (see A319048).
%e A378638 Triangle begins:
%e A378638   n\k| 1  2  3  4  5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20 ...
%e A378638   ----------------------------------------------------------------------------------
%e A378638    1 | 1, 2;
%e A378638    2 | 1, 2, 3, 4, 6;
%e A378638    3 | 1, 2;
%e A378638    4 | 1, 2, 3, 4, 5,  6,  8, 10, 12;
%e A378638    5 | 1, 2;
%e A378638    6 | 1, 2, 3, 4, 6,  7,  9, 14, 18;
%e A378638    7 | 1, 2;
%e A378638    8 | 1, 2, 3, 4, 5,  6,  8, 10, 12, 15, 16, 20, 24, 30;
%e A378638    9 | 1, 2;
%e A378638   10 | 1, 2, 3, 4, 6, 11, 22;
%e A378638   11 | 1, 2;
%e A378638   12 | 1, 2, 3, 4, 5,  6,  7,  8,  9, 10, 12, 13, 14, 18, 21, 26, 28, 36, 42;
%e A378638   13 | 1, 2;
%e A378638   14 | 1, 2, 3, 4, 6;
%e A378638   15 | 1, 2;
%e A378638   16 | 1, 2, 3, 4, 5,  6,  8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 60;
%e A378638   17 | 1, 2;
%e A378638   18 | 1, 2, 3, 4, 6,  7,  9, 14, 18, 19, 27, 38, 54;
%e A378638   19 | 1, 2;
%e A378638   20 | 1, 2, 3, 4, 5,  6,  8, 10, 11, 12, 22, 25, 33, 44, 50, 66;
%e A378638   ...
%t A378638 With[{nmax = 25}, Table[If[OddQ[n], {1, 2}, PositionIndex[Divisible[n, #[[;; Max[n^2, 6]]]]][True]], {n, nmax}] & [EulerPhi[Range[nmax^2]]]]
%o A378638 (PARI) row(n) = select(x->!(n % eulerphi(x)), [1..max(n^2, 6)]); \\ _Michel Marcus_, Dec 05 2024
%Y A378638 Cf. A070633 (row lengths), A319048 (right border), A378639 (row sums).
%Y A378638 Supersequence of A378636.
%Y A378638 Cf. A000010.
%K A378638 nonn,tabf
%O A378638 1,2
%A A378638 _Paolo Xausa_, Dec 03 2024