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

Author

Arkadiusz Wesolowski, Mar 05 2014

Keywords

• nonn
• fini
• full

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

Examples

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

Links

• 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

Crossrefs

Cf. A201644, A239036.