A391387 Irregular triangle read by rows: greatest odd divisor of A391261(n,k), signed; 0 if A391261(n,k) = 0.

1, 1, 0, 1, -1, 1, 0, -1, 1, -1, -1, 1, 0, -3, 1, -1, -1, 1, 1, 0, -1, 0, 1, 1, 0, -3, -1, 1, 0, -5, 0, 5, 1, -1, -1, 3, 3, -1, 1, 0, -1, 0, 1, 1, -1, -5, 1, 3, -3, -1, 1, 0, -7, 0, 7, 0, -7, 1, 1, -1, -1, 1, 1, 0, -1, 0, 5, 0, -1, 0, 1, 1, -1, -7, 3, 15, -5, -5, 1, 1

Offset

1,14

Comments

The row length is given by A055034(n)+1 = A389480(n,1)+1, n > 1.

Remaining number after factoring out the powers of 2 from A391261(n,k), from which it becomes clear that we defined the greatest odd divisor of 0 to be 0.

Links

Table of n, a(n) for n=1..80.

Formula

T(n,k) = A391261(n,k)/2^A391386(n,k).

Example

The 10th row of A391261 is 16, 0, -20, 0, 5; 16 = 2^4*1, 0 = 2^0*0, -20 = 2^2*(-5), 0 = 2^0*0 and 5 = 2^0*5, so row 10 becomes 1, 0, -5, 0, 5.
Triangle begins (0 <= k <= A055034(n)):
   n\k   0     1     2     3     4     5     6     7     8     9
   1     1
   2     1     0
   3     1    -1
   4     1     0    -1
   5     1    -1    -1
   6     1     0    -3
   7     1    -1    -1     1
   8     1     0    -1     0     1
   9     1     0    -3    -1
  10     1     0    -5     0     5
  11     1    -1    -1     3     3    -1
  12     1     0    -1     0     1
  13     1    -1    -5     1     3    -3    -1
  14     1     0    -7     0     7     0    -7
  15     1     1    -1    -1     1
  16     1     0    -1     0     5     0    -1     0     1
  17     1    -1    -7     3    15    -5    -5     1     1
  18     1     0    -3     0     9     0    -3
  19     1    -1    -1     7    21   -15    -5     5     5    -1
  20     1     0    -1     0    19     0    -3     0     1

Crossrefs

Cf. A000265, A055034, A389480, A391261, A391386.

Sequence in context: A304222 A134108 A387502 * A176851 A205535 A172972

Adjacent sequences: A391384 A391385 A391386 * A391388 A391389 A391390

Keyword

sign,tabf

Author

A.H.M. Smeets, Dec 08 2025

Status

approved