A111809 Triangle read by rows: for T(n,k), 1<=k<=n, gcd(k,n)=1, consider all representations of k/n as an Egyptian fraction; T(n,k) = minimal value of sum of denominators.

1, 2, 3, 8, 4, 6, 5, 18, 12, 17, 6, 5, 7, 32, 39, 16, 23, 36, 8, 12, 10, 14, 9, 24, 12, 20, 17, 23, 10, 15, 7, 20, 11, 72, 48, 36, 47, 24, 35, 95, 72, 60, 12, 10, 7, 12, 13, 98, 71, 82, 95, 101, 28, 41, 47, 58, 71, 96, 14, 21, 34, 9, 34, 41, 15, 32, 16, 21, 8, 23, 13, 15, 16, 24, 20

Offset

1,2

Comments

Apart from an additional first row the same as A100869. - R. J. Mathar, May 25 2026

Row n has A000010(n) terms. - David Wasserman, Mar 03 2009

References

Franklin T. Adams-Watters, Posting to Seq Fan mailing list, Aug 21 2004

Links

Table of n, a(n) for n=1..75.

Index entries for sequences related to Egyptian fractions

Example

Triangle begins:
  1
  2
  3 8
  4 6
  5 18 12 17
  6 5
  7 32 39 16 23 36
  8 12 10 14
  9 24 12 20 17 23
  10 15 7 20
  11 72 48 36 47 24 35 95 72 60
  12 10 7 12

Crossrefs

Cf. A097847, A097848, A097849, A111807, A111804, A100871.

Sequence in context: A195794 A145605 A275708 * A100869 A110142 A158928

Adjacent sequences: A111806 A111807 A111808 * A111810 A111811 A111812

Keyword

nonn,tabf,changed

Author

N. J. A. Sloane, based on communications from Franklin T. Adams-Watters, Nov 22 2005

Extensions

Corrected and extended by David Wasserman, Mar 03 2009

T(15, 14) corrected by David Wasserman, Mar 19 2009

Status

approved