

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).


6



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

Table of n, a(n) for n=1..63.
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) 117130.
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+11)*(1/1+1/11/1)=1.
a(2)=(1+1+1)*(1/1+1/1+1/1)=9.
a(9)=(215+78)*(1/21/15+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 A045522
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



