A357372 Square array A(n, k), n, k > 0, read by antidiagonals; A(n, k) is the numerator of 1/n + 1/k.

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

Offset

1,1

Comments

See A257522 for the corresponding denominators.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10011

Formula

A(n, k) = (n + k) / gcd(n + k, n*k).

A(n, k) = A(k, n).

A(n, 1) = n + 1.

A(n, n) = A000034(n).

A(n, n+1) = 2*n + 1.

Example

Array A(n, k) begins:
  n\k |  1   2   3   4   5   6   7   8   9  10  11  12  13
  ----+---------------------------------------------------
    1 |  2   3   4   5   6   7   8   9  10  11  12  13  14
    2 |  3   1   5   3   7   2   9   5  11   3  13   7  15
    3 |  4   5   2   7   8   1  10  11   4  13  14   5  16
    4 |  5   3   7   1   9   5  11   3  13   7  15   1  17
    5 |  6   7   8   9   2  11  12  13  14   3  16  17  18
    6 |  7   2   1   5  11   1  13   7   5   4  17   1  19
    7 |  8   9  10  11  12  13   2  15  16  17  18  19  20
    8 |  9   5  11   3  13   7  15   1  17   9  19   5  21
    9 | 10  11   4  13  14   5  16  17   2  19  20   7  22
   10 | 11   3  13   7   3   4  17   9  19   1  21  11  23
   11 | 12  13  14  15  16  17  18  19  20  21   2  23  24
   12 | 13   7   5   1  17   1  19   5   7  11  23   1  25
   13 | 14  15  16  17  18  19  20  21  22  23  24  25   2

Mathematica

Flatten[Table[Numerator[1/i + 1/(m - i)], {m, 13}, {i, m - 1}]]

Prog

(PARI) A(n, k) = numerator(1/n + 1/k)

Crossrefs

Cf. A000034, A257522.

Sequence in context: A060573 A279086 A337307 * A316910 A251715 A361819

Adjacent sequences: A357369 A357370 A357371 * A357373 A357374 A357375

Keyword

nonn,tabl,easy,frac

Author

Rémy Sigrist, Sep 25 2022

Status

approved