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).

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, 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, 1, 2, 1, 2, 3, 4, 6, 7, 9, 14, 18, 1, 2, 1, 2, 3, 4, 5, 6, 8, 10, 11, 12

Offset

1,3

Comments

If n = 2 or an odd number >= 3, row n is {1, 2}.

If n is an even number >= 4, row n begins with {1, 2, 3, 4}.

Links

Paolo Xausa, Table of n, a(n) for n = 1..11226 (rows 1..1000 of triangle, flattened).

Example

Triangle begins:
  n\k| 1  2  3  4  5  6  7   8   9  10  11 ...
  --------------------------------------------
   1 | 1;
   2 | 1, 2;
   3 | 1, 2;
   4 | 1, 2, 3, 4;
   5 | 1, 2;
   6 | 1, 2, 3, 4, 6;
   7 | 1, 2;
   8 | 1, 2, 3, 4, 5, 6, 8;
   9 | 1, 2;
  10 | 1, 2, 3, 4, 6;
  11 | 1, 2;
  12 | 1, 2, 3, 4, 5, 6, 7,  8,  9, 10, 12;
  13 | 1, 2;
  14 | 1, 2, 3, 4, 6;
  15 | 1, 2;
  16 | 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16;
  17 | 1, 2;
  18 | 1, 2, 3, 4, 6, 7, 9, 14, 18;
  19 | 1, 2;
  20 | 1, 2, 3, 4, 5, 6, 8, 10, 11, 12;
  ...

Mathematica

With[{nmax = 25}, Table[If[OddQ[n] && n > 2, {1, 2}, PositionIndex[Divisible[n, #[[;; n]]]][True]], {n, nmax}] & [EulerPhi[Range[nmax]]]]

Prog

(PARI) row(n) = select(x->!(n % eulerphi(x)), [1..n]); \\ Michel Marcus, Dec 05 2024

Crossrefs

Cf. A069932 (row lengths), A362469 (row sums), A378637 (right border).

Subsequence of A378638.

Cf. A000010.

Sequence in context: A175851 A049711 A137293 * A366254 A177803 A274080

Adjacent sequences: A378632 A378633 A378634 * A378637 A378638 A378639

Keyword

nonn,tabf,easy,new

Author

Paolo Xausa, Dec 02 2024

Status

approved