A102535 Integers n such that -n is 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).

4, 10, 11, 12, 18, 19, 20, 22, 25, 28, 29, 30, 31, 32, 36, 39, 40, 42, 43, 44, 48, 50, 51, 52, 54, 56, 58, 59, 61, 67, 69, 70, 72, 76, 78, 84, 85, 86, 88, 89, 91, 92, 95, 96, 100, 101, 102, 103, 104, 105, 107, 108, 109, 112, 113, 115, 116, 120, 122, 123

Offset: 1

Author

N. J. A. Sloane, Mar 17 2005

Keywords

• nonn

Comments

Also numbers k such that A309144(k) > 0. - Seiichi Manyama, Jul 14 2019

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 1 <= n <= 1000 (copy from MacLeod's website)

Crossrefs

Cf. A085514, A102778, A102779, A102809, A309144.