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

Author

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

Keywords

• nonn
• tabf
• changed

Comments

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

Examples

			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
		

References

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

Links

• Index entries for sequences related to Egyptian fractions

Crossrefs

Cf. A097847, A097848, A097849, A111807, A111804, A111860.

Extensions

Corrected and extended by David Wasserman, Mar 03 2009

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