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

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Last modified January 20 08:18 EST 2020. Contains 331081 sequences. (Running on oeis4.)