A085514 Integers n representable as the product of the sum of three nonzero integers with the sum of their reciprocals: n=(x+y+z)*(1/x+1/y+1/z).
1, 9, 10, 11, 14, 15, 18, 26, 29, 30, 31, 34, 35, 37, 38, 42, 43, 44, 48, 52, 53, 54, 55, 57, 59, 62, 63, 64, 67, 69, 70, 71, 73, 74, 75, 76, 82, 84, 85, 86, 90, 92, 93, 94, 95, 96, 98, 100, 101, 102, 103, 105, 106, 108, 111, 112, 116, 117, 122, 125, 126, 127, 128
Offset: 1
Keywords
Examples
a(1)=1 because (1+1-1)*(1/1+1/1-1/1)=1. a(2)=(1+1+1)*(1/1+1/1+1/1)=9. a(9)=(2-15+78)*(1/2-1/15+1/78)=29.
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..1000
- A. Bremner, R. K. Guy and R. Nowakowski, Which integers are representable as the product of the sum of three integers with the sum of their reciprocals?, Math. Comp. 61 (1993) 117-130.
- Allan J. MacLeod, Knight's Problem
- Allan J. MacLeod, Solutions for 11 <= n <= 999 (copy from MacLeod's website)
- Nguyen Xuan Tho, What positive integers n can be presented in the form n = (x + y + z)(1/x + 1/y + 1/z)?, Annales Mathematicae et Informaticae 54 (2021).
Crossrefs
Extensions
Corrected and extended by David J. Rusin, Jul 30 2003
More terms from the MacLeod web site, Mar 17 2005
Comments