A073546 Triangle read by rows: row n gives denominators of n distinct unit fractions (or Egyptian fractions) summing to 1, where denominators are listed in increasing order and the largest denominator is smallest possible.

2, 3, 6, 2, 4, 6, 12, 2, 4, 10, 12, 15, 3, 4, 6, 10, 12, 15, 3, 4, 9, 10, 12, 15, 18, 3, 5, 9, 10, 12, 15, 18, 20, 4, 5, 8, 9, 10, 15, 18, 20, 24, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 5, 6, 8, 9, 10, 15, 18, 20, 21, 24, 28, 6, 7, 8, 9, 10, 14, 15, 18, 20, 24, 28, 30

Offset

3,1

References

Mohammad K. Azarian, Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330. Solution published in Vol. 43, No. 4, September 2012, pp. 340-342

R. K. Guy, Unsolved Problems in Number Theory, 2nd Edition, page 161.

Links

Table of n, a(n) for n=3..77.

K. S. Brown, Unit Fractions, smallest last term

Example

n=3: 2,3,6;
n=4: 2,4,6,12;
n=5: 2,4,10,12,15;
n=6: 3,4,6,10,12,15;
...

Crossrefs

Sequence in context: A224910 A275734 A216993 * A216975 A275666 A330666

Adjacent sequences: A073543 A073544 A073545 * A073547 A073548 A073549

Keyword

nonn,tabf

Author

Robert G. Wilson v, Aug 27 2002

Extensions

Edited by Max Alekseyev, Mar 01 2018

Status

approved