A097848 -id:A097848

A097849

Maximal entry in row n of A097847 (or equally A097848).

+20
7

1, 1, 2, 2, 3, 2, 3, 3, 3, 3, 4, 3, 4, 4, 3, 4, 5, 3, 4, 3, 4, 4, 5, 3, 4, 4, 4, 4, 5, 4, 5, 4, 4, 5, 4, 4, 5, 5, 5, 4, 5, 4, 5, 4, 4, 5, 5, 4, 5, 5, 5, 5, 5, 4, 5, 4, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 5, 5, 4, 5, 4, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 6, 5, 4

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

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..105.

Index entries for sequences related to Egyptian fractions

KEYWORD

nonn

AUTHOR

Franklin T. Adams-Watters, Aug 31 2004

STATUS

approved

A097847

Triangle read by rows: T(n,k) = minimal number of terms needed to write k/n (for 1 <= k <= n) as a sum of unit fractions.

+10
8

1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 1, 1, 2, 3, 2, 3, 3, 1, 1, 1, 2, 1, 2, 2, 3, 1, 1, 2, 1, 2, 2, 2, 3, 3, 1, 1, 1, 2, 2, 1, 2, 2, 3, 3, 1, 1, 2, 2, 2, 3, 2, 3, 4, 4, 4, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 1, 1, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 4, 1, 1, 1, 2, 2, 2, 3, 1, 2

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

OFFSET

1,5

LINKS

Table of n, a(n) for n=1..99.

Index entries for sequences related to Egyptian fractions

FORMULA

T(n, n-1) = A330808(n). - Jon E. Schoenfield, Jan 11 2020

EXAMPLE

Triangle begins:

1

1 1

1 2 1

1 1 2 1

1 2 2 3 1

1 1 1 2 2 1

1 2 3 2 3 3 1

1 1 2 1 2 2 3 1

1 2 1 2 2 2 3 3 1

1 1 2 2 1 2 2 3 3 1

1 2 2 2 3 2 3 4 4 4 1

CROSSREFS

Cf. A097848, A097849, A330808.

Row sums give A270429.

KEYWORD

nonn,tabl

AUTHOR

Franklin T. Adams-Watters, Aug 31 2004

STATUS

approved

A111860

a(n) = maximal value in row n of A111809.

+10
4

1, 2, 8, 6, 18, 6, 39, 14, 24, 20, 95, 12, 101, 41, 32, 30, 160, 26, 198, 27, 50, 94, 276, 24, 96, 103, 80, 42, 394, 30, 382, 62, 91, 165, 72, 36, 594, 200, 106, 54, 548, 45, 632, 93, 96, 278, 719, 48, 283, 98, 165, 104, 872, 78, 132, 75, 206, 392, 1020, 60, 1128, 384

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

OFFSET

1,2

REFERENCES

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

LINKS

Table of n, a(n) for n=1..62.

Index entries for sequences related to Egyptian fractions

CROSSREFS

Cf. A097847, A097848, A097849, A111804, A111809, A111860.

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

Corrected and extended by David Wasserman, Mar 20 2009

STATUS

approved

A111804

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 maximal denominator.

+10
3

1, 2, 3, 6, 4, 4, 5, 15, 10, 10, 6, 3, 7, 21, 21, 14, 14, 21, 8, 8, 8, 8, 9, 18, 9, 18, 9, 18, 10, 10, 5, 15, 11, 44, 44, 33, 33, 22, 22, 44, 44, 33, 12, 6, 4, 6, 13, 65, 39, 39, 52, 52, 26, 26, 39, 39, 52, 65, 14, 14, 21, 7, 21, 21, 15, 20, 10, 10, 5, 15, 6, 10, 16, 16, 16, 16, 16, 16

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

OFFSET

1,2

REFERENCES

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

LINKS

Table of n, a(n) for n=1..78.

Index entries for sequences related to Egyptian fractions

EXAMPLE

Triangle begins:

1

2

3 6

4 4

5 15 10 10

6 3

7 21 21 14 14 21

8 8 8 8

9 18 9 18 9 18

10 10 5 15

11 44 44 33 33 22 22 44 44 33

12 6 4 6

13 65 39 39 65 52 26 26 39 39 52 65

CROSSREFS

Cf. A097847, A097848, A097849, A111807, A111809, A111860.

KEYWORD

nonn,tabf

AUTHOR

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

EXTENSIONS

One term corrected by David Wasserman, Feb 17 2009

STATUS

approved

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.

+10
3

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

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

OFFSET

1,2

COMMENTS

Comment from David Wasserman, Mar 03 2009: Row n has A000010(n) members.

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, A111860.

KEYWORD

nonn,tabf

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

A111807

a(n) = maximal value in row n of A111804.

+10
2

1, 2, 6, 4, 15, 6, 21, 8, 18, 15, 44, 12, 65, 21, 20, 16, 85, 18, 114, 20, 35, 44, 138, 24, 75, 65, 54, 28, 174, 30, 186, 32, 66, 85, 42, 36, 296, 114, 65, 40, 287, 42, 301, 44, 45, 138, 376, 48, 147, 75, 102, 65, 371, 54, 88, 56, 114, 174, 413, 60, 488, 186, 72, 64, 117, 66

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

OFFSET

1,2

REFERENCES

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

LINKS

Table of n, a(n) for n=1..66.

Index entries for sequences related to Egyptian fractions

CROSSREFS

Cf. A097847, A097848, A097849, A111804, A111809, A111860.

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

More terms from David Wasserman, Feb 18 2009

STATUS

approved