A238795 The unique set of eleven distinct positive odd numbers up to 105 the sum of whose reciprocals is 1.

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

Offset

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..11.

R. Arce-Nazario, F. Castro, and R. Figueroa, On the number of solutions of Sum_{i = 1..11} 1/x_i = 1 in distinct odd natural numbers, J. Number Theory, 133 (2013), pp. 2036-2046.

Index entries for sequences related to Egyptian fractions

Example

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

Crossrefs

Cf. A201644, A239036.

Sequence in context: A264734 A004156 A081936 * A265079 A092361 A029950

Adjacent sequences: A238792 A238793 A238794 * A238796 A238797 A238798

Keyword

nonn,fini,full

Author

Arkadiusz Wesolowski, Mar 05 2014

Status

approved