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A378636 Irregular triangle read by rows: row n lists all m <= n such that phi(m) divides n, where phi is the Euler totient function (A000010).

%I A378636 #30 Dec 06 2024 11:31:06
%S A378636 1,1,2,1,2,1,2,3,4,1,2,1,2,3,4,6,1,2,1,2,3,4,5,6,8,1,2,1,2,3,4,6,1,2,
%T A378636 1,2,3,4,5,6,7,8,9,10,12,1,2,1,2,3,4,6,1,2,1,2,3,4,5,6,8,10,12,15,16,
%U A378636 1,2,1,2,3,4,6,7,9,14,18,1,2,1,2,3,4,5,6,8,10,11,12
%N A378636 Irregular triangle read by rows: row n lists all m <= n such that phi(m) divides n, where phi is the Euler totient function (A000010).
%C A378636 If n = 2 or an odd number >= 3, row n is {1, 2}.
%C A378636 If n is an even number >= 4, row n begins with {1, 2, 3, 4}.
%H A378636 Paolo Xausa, <a href="/A378636/b378636.txt">Table of n, a(n) for n = 1..11226</a> (rows 1..1000 of triangle, flattened).
%e A378636 Triangle begins:
%e A378636   n\k| 1  2  3  4  5  6  7   8   9  10  11 ...
%e A378636   --------------------------------------------
%e A378636    1 | 1;
%e A378636    2 | 1, 2;
%e A378636    3 | 1, 2;
%e A378636    4 | 1, 2, 3, 4;
%e A378636    5 | 1, 2;
%e A378636    6 | 1, 2, 3, 4, 6;
%e A378636    7 | 1, 2;
%e A378636    8 | 1, 2, 3, 4, 5, 6, 8;
%e A378636    9 | 1, 2;
%e A378636   10 | 1, 2, 3, 4, 6;
%e A378636   11 | 1, 2;
%e A378636   12 | 1, 2, 3, 4, 5, 6, 7,  8,  9, 10, 12;
%e A378636   13 | 1, 2;
%e A378636   14 | 1, 2, 3, 4, 6;
%e A378636   15 | 1, 2;
%e A378636   16 | 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16;
%e A378636   17 | 1, 2;
%e A378636   18 | 1, 2, 3, 4, 6, 7, 9, 14, 18;
%e A378636   19 | 1, 2;
%e A378636   20 | 1, 2, 3, 4, 5, 6, 8, 10, 11, 12;
%e A378636   ...
%t A378636 With[{nmax = 25}, Table[If[OddQ[n] && n > 2, {1, 2}, PositionIndex[Divisible[n, #[[;; n]]]][True]], {n, nmax}] & [EulerPhi[Range[nmax]]]]
%o A378636 (PARI) row(n) = select(x->!(n % eulerphi(x)), [1..n]); \\ _Michel Marcus_, Dec 05 2024
%Y A378636 Cf. A069932 (row lengths), A362469 (row sums), A378637 (right border).
%Y A378636 Subsequence of A378638.
%Y A378636 Cf. A000010.
%K A378636 nonn,tabf,easy
%O A378636 1,3
%A A378636 _Paolo Xausa_, Dec 02 2024