A289172 Irregular triangle read by rows: row n lists terms m of A038566(n) such that A001221(m) = A051265(n), with a(1) = 1.

1, 1, 2, 3, 2, 3, 4, 5, 6, 3, 5, 7, 2, 4, 5, 7, 8, 3, 7, 9, 6, 10, 5, 7, 11, 6, 10, 12, 3, 5, 9, 11, 13, 14, 15, 6, 10, 12, 14, 15, 5, 7, 11, 13, 17, 6, 10, 12, 14, 15, 18, 3, 7, 9, 11, 13, 17, 19, 10, 20, 15, 21, 6, 10, 12, 14, 15, 18, 20, 21, 22, 5, 7, 11

Offset: 1

Author

Michael De Vlieger, Aug 11 2017

Keywords

• nonn
• easy
• tabf

Comments

Consider A051265(n), the largest value of A001221(m) for 1 <= m <= n such that gcd(m, n) = 1 (i.e., m is in the reduced residue system or RRS of n, or m is a totative of n). Row n of this sequence consists of m in RRS(n) such that omega(m) = A051265(n).

Examples

			Triangle begins:
   n    T(n,m)                        A051265(n)
   1:   1                                     0
   2:   1                                     0
   3:   2                                     1
   4:   3                                     1
   5:   2    3    4                           1
   6:   5                                     1
   7:   6                                     2
   8:   3    5    7                           1
   9:   2    4    5    7    8                 1
  10:   3    7    9                           1
  11:   6   10                                2
  12:   5    7   11                           1
  13:   6   10   12                           2
  14:   3    5    9   11   13                 1
  15:  14                                     2
  16:  15                                     2
  17:   6   10   12   14   15                 2
  18:   5    7   11   13   17                 1
  19:   6   10   12   14   15   18            2
  20:   3    7    9   11   13   17   19       1
		

Links

• Michael De Vlieger, Table of n, a(n) for the first 1000 rows, flattened

Crossrefs

Cf. A001221, A002110, A038566, A048597, A051250, A051265, A051266, A051267, A051268.

Programs

Mathematica

Table[MaximalBy[#, Last][[All, 1]] &@ Map[{#, PrimeNu@ #} &, Cases[Range[n - 1], k_ /; CoprimeQ[n, k]]] /. {} -> {1}, {n, 30}] // Flatten (* Michael De Vlieger, Aug 11 2017 *)