

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
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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 8385.


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



