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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.

%I A260819 #33 Feb 16 2025 08:33:26
%S A260819 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,
%T A260819 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
%N 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.
%C A260819 There are only 14 positive integer solutions for 1/a + 1/b + 1/c + 1/d = 1.
%D A260819 W. Sierpiński, 250 problems in elementary number theory, Elsevier Science Ltd, pages 14 and 83-85.
%H A260819 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EgyptianFraction.html">Egyptian Fraction</a>
%H A260819 <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%e A260819 The 2nd row is [2,3,8,24] and represents the solution 1/2 + 1/3 + 1/8 + 1/24 = 1.
%e A260819 List of all the solutions:
%e A260819 1/2 + 1/3 + 1/7  + 1/42 = 1
%e A260819 1/2 + 1/3 + 1/8  + 1/24 = 1
%e A260819 1/2 + 1/3 + 1/9  + 1/18 = 1
%e A260819 1/2 + 1/3 + 1/10 + 1/15 = 1
%e A260819 1/2 + 1/3 + 1/12 + 1/12 = 1
%e A260819 1/2 + 1/4 + 1/5  + 1/20 = 1
%e A260819 1/2 + 1/4 + 1/6  + 1/12 = 1
%e A260819 1/2 + 1/4 + 1/8  + 1/8  = 1
%e A260819 1/2 + 1/5 + 1/5  + 1/10 = 1
%e A260819 1/2 + 1/6 + 1/6  + 1/6  = 1
%e A260819 1/3 + 1/3 + 1/4  + 1/12 = 1
%e A260819 1/3 + 1/3 + 1/6  + 1/6  = 1
%e A260819 1/3 + 1/4 + 1/4  + 1/6  = 1
%e A260819 1/4 + 1/4 + 1/4  + 1/4  = 1
%Y A260819 Cf. A229941.
%K A260819 easy,full,fini,nonn,tabf
%O A260819 1,1
%A A260819 _Marco Ripà_, Jul 31 2015