A357372 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

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