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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). 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
See under A086446 for comments and references.
LINKS
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
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

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Last modified February 21 13:52 EST 2024. Contains 370235 sequences. (Running on oeis4.)