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

Author

Paolo Xausa, Dec 02 2024

Keywords

• nonn
• tabf
• easy

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}.

Examples

			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;
  ...
		

Links

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

Crossrefs

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

Subsequence of A378638.

Cf. A000010.

Programs

Mathematica

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

PARI

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