A100870 Triangle read by rows: T(n,k) = minimal sum of denominators needed to write k/n as a sum of distinct unit fractions, 1 <= k <= n-1.

2, 3, 8, 4, 2, 6, 5, 18, 12, 17, 6, 3, 2, 8, 5, 7, 32, 39, 16, 23, 36, 8, 4, 12, 2, 10, 6, 14, 9, 24, 3, 12, 20, 8, 17, 23, 10, 5, 15, 18, 2, 12, 7, 17, 20, 11, 72, 48, 36, 47, 24, 35, 95, 72, 60, 12, 6, 4, 3, 10, 2, 7, 8, 6, 5, 12, 13, 98, 71, 82, 95, 101, 28, 41, 47, 58, 71, 96, 14, 7

Offset

2,1

Links

Table of n, a(n) for n=2..81.

Index entries for sequences related to Egyptian fractions

Example

Triangle begins:
  n\k|  1  2  3  4  5  6  7  8  9 10 11
  ---+---------------------------------
   2 |  2
   3 |  3  8
   4 |  4  2  6
   5 |  5 18 12 17
   6 |  6  3  2  8  5
   7 |  7 32 39 16 23 36
   8 |  8  4 12  2 10  6 14
   9 |  9 24  3 12 20  8 17 23
  10 | 10  5 15 18  2 12  7 17 20
  11 | 11 72 48 36 47 24 35 95 72 60
  12 | 12  6  4  3 10  2  7  8  6  5 12
  ...
T(5,2) = 18 because the minimal sum of unit fractions is 2/5 = 1/3 + 1/15 and 3+15 = 18.

Crossrefs

Cf. A097847, A100869, A100871.

Sequence in context: A293273 A349003 A079555 * A386990 A210688 A328428

Adjacent sequences: A100867 A100868 A100869 * A100871 A100872 A100873

Keyword

nonn,tabl

Author

Franklin T. Adams-Watters, Nov 20 2004

Extensions

Name clarified by Pontus von Brömssen, May 26 2026

Status

approved