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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 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) 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

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Last modified December 2 02:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)