A260819 Positive integer solutions [a',b',c',d'] of the equation 1/a + 1/b + 1/c + 1/d = 1, for a <= b <= c <= d, lexicographically sorted.

2, 3, 7, 42, 2, 3, 8, 24, 2, 3, 9, 18, 2, 3, 10, 15, 2, 3, 12, 12, 2, 4, 5, 20, 2, 4, 6, 12, 2, 4, 8, 8, 2, 5, 5, 10, 2, 6, 6, 6, 3, 3, 4, 12, 3, 3, 6, 6, 3, 4, 4, 6, 4, 4, 4, 4

Offset

1,1

Comments

There are only 14 positive integer solutions for 1/a + 1/b + 1/c + 1/d = 1.

References

W. Sierpiński, 250 problems in elementary number theory, Elsevier Science Ltd, pages 14 and 83-85.

Links

Table of n, a(n) for n=1..56.

Eric Weisstein's World of Mathematics, Egyptian Fraction

Index entries for sequences related to Egyptian fractions

Example

The 2nd row is [2,3,8,24] and represents the solution 1/2 + 1/3 + 1/8 + 1/24 = 1.
List of all the solutions:
1/2 + 1/3 + 1/7  + 1/42 = 1
1/2 + 1/3 + 1/8  + 1/24 = 1
1/2 + 1/3 + 1/9  + 1/18 = 1
1/2 + 1/3 + 1/10 + 1/15 = 1
1/2 + 1/3 + 1/12 + 1/12 = 1
1/2 + 1/4 + 1/5  + 1/20 = 1
1/2 + 1/4 + 1/6  + 1/12 = 1
1/2 + 1/4 + 1/8  + 1/8  = 1
1/2 + 1/5 + 1/5  + 1/10 = 1
1/2 + 1/6 + 1/6  + 1/6  = 1
1/3 + 1/3 + 1/4  + 1/12 = 1
1/3 + 1/3 + 1/6  + 1/6  = 1
1/3 + 1/4 + 1/4  + 1/6  = 1
1/4 + 1/4 + 1/4  + 1/4  = 1

Crossrefs

Cf. A229941.

Sequence in context: A119662 A265776 A163157 * A000945 A261564 A126263

Adjacent sequences: A260816 A260817 A260818 * A260820 A260821 A260822

Keyword

easy,full,fini,nonn,tabf

Author

Marco Ripà, Jul 31 2015

Status

approved