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

1,2

Comments

See under A086446 for comments and references.

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).

Example

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.

Crossrefs

Cf. A086446 (representation by positive x, y, z), A102535 (representable negative n)

See A102774, A102775, A102777 for values of x, y, z corresponding to values of n >= 11.

Sequence in context: A120193 A134534 A125004 * A086446 A168042 A342147

Adjacent sequences: A085511 A085512 A085513 * A085515 A085516 A085517

Keyword

nonn

Author

Hugo Pfoertner, Jul 19 2003

Extensions

Corrected and extended by David J. Rusin, Jul 30 2003

More terms from the MacLeod web site, Mar 17 2005

Status

approved