A384244 Triangle in which the n-th row gives the numbers k from 1 to n such that the greatest common unitary divisor of k and n is 1.

1, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 1, 3, 4, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 5, 7, 8, 9, 10, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 3, 4, 5, 8, 9, 11, 12, 13, 1, 2, 4, 7, 8, 9, 11, 13, 14

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10349 (first 160 rows flattened)

László Tóth, On the Bi-Unitary Analogues of Euler's Arithmetical Function and the Gcd-Sum Function, Journal of Integer Sequences, Vol. 12 (2009), Article 09.5.2.

Example

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

Mathematica

udiv[n_] := Select[Divisors[n], CoprimeQ[#, n/#] &];
ugcd[n_, m_] := Max[Intersection[udiv[n], udiv[m]]];
row[n_] := Select[Range[n], ugcd[n, #] == 1 &]; Array[row, 15] // Flatten

Prog

(PARI) udiv(n) = select(x -> gcd(x, n/x) == 1, divisors(n));
ugcd(n, m) = vecmax(setintersect(udiv(n), udiv(m)));
row(n) = select(x -> ugcd(n, x) == 1, vector(n, i, i));

Crossrefs

The bi-unitary analog of A038566.

Cf. A116550 (row lengths), A200723 (row sums), A077610, A089912, A165430, A225174, A064379 (infinitary analog), A384046 (unitary analog).

Sequence in context: A391926 A066019 A051237 * A064379 A384046 A278961

Adjacent sequences: A384241 A384242 A384243 * A384245 A384246 A384247

Keyword

nonn,tabf,easy

Author

Amiram Eldar, May 23 2025

Status

approved