A238795 - OEIS

%I #23 Feb 16 2024 05:47:00

%S 3,5,7,9,11,33,35,45,55,77,105

%N The unique set of eleven distinct positive odd numbers up to 105 the sum of whose reciprocals is 1.

%C For any set of distinct numbers whose reciprocals sum to 1, the largest must be neither a prime nor a prime power.

%C For sets of 11 distinct positive odd numbers, relaxing the a(11) <= 105 constraint allows a second solution at 115 (3, 5, 7, 9, 15, 21, 23, 45, 69, 105, 115), a third at 117 (3, 5, 7, 9, 13, 21, 35, 39, 63, 105, 117), 3 more at 135, 2 more at 143, and 2 more at 165. - _Jon E. Schoenfield_, Mar 07 2014

%H R. Arce-Nazario, F. Castro, and R. Figueroa, <a href="https://doi.org/10.1016/j.jnt.2012.11.011">On the number of solutions of Sum_{i = 1..11} 1/x_i = 1 in distinct odd natural numbers</a>, J. Number Theory, 133 (2013), pp. 2036-2046.

%H <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>

%e 1/3 + 1/5 + 1/7 + 1/9 + 1/11 + 1/33 + 1/35 + 1/45 + 1/55 + 1/77 + 1/105 = 1.

%Y Cf. A201644, A239036.

%K nonn,fini,full

%O 1,1

%A _Arkadiusz Wesolowski_, Mar 05 2014