A384047 Triangle read by rows: T(n, k) for 1 <= k <= n is the largest divisor of k that is a unitary divisor of n.

1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 1, 5, 1, 2, 3, 2, 1, 6, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 3, 4, 1, 3, 1, 4, 3, 1, 1, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10585 (first 145 rows flattened)

Formula

T(n, 1) = 1.

T(n, n) = n.

T(n, k) <= A050873(n, k) = gcd(n, k), with equality if n is squarefree (A005117).

Example

Triangle begins:
  1
  1, 2
  1, 1, 3
  1, 1, 1, 4
  1, 1, 1, 1, 5
  1, 2, 3, 2, 1, 6
  1, 1, 1, 1, 1, 1, 7
  1, 1, 1, 1, 1, 1, 1, 8
  1, 1, 1, 1, 1, 1, 1, 1, 9
  1, 2, 1, 2, 5, 2, 1, 2, 1, 10

Mathematica

udiv[n_] := Select[Divisors[n], CoprimeQ[#, n/#] &]; T[n_, k_] := Max[Intersection[udiv[n], Divisors[k]]]; Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten

Prog

(PARI) udiv(n) = select(x -> gcd(x, n/x) == 1, divisors(n));
T(n, k) = vecmax(setintersect(udiv(n), divisors(k)));

Crossrefs

Cf. A005117, A050873, A077610, A145388 (row sums), A165430, A225174, A384046.

Upper right triangle of A322482.

Sequence in context: A167407 A216764 A165430 * A384245 A334215 A164823

Adjacent sequences: A384044 A384045 A384046 * A384048 A384049 A384050

Keyword

nonn,tabl,easy

Author

Amiram Eldar, May 18 2025

Status

approved