A384446 Triangle read by rows: T(n, k) = |gcd(n, k) - k|.

0, 1, 0, 2, 0, 0, 3, 0, 1, 0, 4, 0, 0, 2, 0, 5, 0, 1, 2, 3, 0, 6, 0, 0, 0, 2, 4, 0, 7, 0, 1, 2, 3, 4, 5, 0, 8, 0, 0, 2, 0, 4, 4, 6, 0, 9, 0, 1, 0, 3, 4, 3, 6, 7, 0, 10, 0, 0, 2, 2, 0, 4, 6, 6, 8, 0, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 12, 0, 0, 0, 0, 4, 0, 6, 4, 6, 8, 10, 0

Offset

0,4

Comments

T(n, k) can be understood as a measure of the divisibility of n by k.

Links

Table of n, a(n) for n=0..90.

Formula

T(n, 0) = n.

T(n, k) = 0 if k divides n, in particular T(n, 1) = T(n, n) = 0.

T(n, k) = |A002262(n, k) - A109004(n, k)|.

Example

Triangle starts:
  [0] [0]
  [1] [1, 0]
  [2] [2, 0, 0]
  [3] [3, 0, 1, 0]
  [4] [4, 0, 0, 2, 0]
  [5] [5, 0, 1, 2, 3, 0]
  [6] [6, 0, 0, 0, 2, 4, 0]
  [7] [7, 0, 1, 2, 3, 4, 5, 0]
  [8] [8, 0, 0, 2, 0, 4, 4, 6, 0]
  [9] [9, 0, 1, 0, 3, 4, 3, 6, 7, 0]

Prog

(Python)
from math import gcd
print([abs(gcd(n, k) - k) for n in range(13) for k in range(n + 1)])

Crossrefs

Cf. A002262, A109004, A372727.

Sequence in context: A212195 A228926 A372727 * A321414 A268865 A024159

Adjacent sequences: A384443 A384444 A384445 * A384447 A384448 A384449

Keyword

nonn,tabl

Author

Peter Luschny, May 29 2025

Status

approved