A257841 z-value of the lexicographically first solution (x,y,z) of 4/n = 1/x + 1/y + 1/z with 0 < x < y < z all integers, or 0 if there is no such solution. Corresponding x and y values are in A257839 and A257840.

0, 0, 12, 6, 20, 42, 210, 42, 90, 240, 1122, 156, 468, 812, 3660, 420, 510, 2070, 9120, 930, 1806, 4422, 19182, 1806, 2100, 8372, 35910, 3192, 9048, 14520, 61752, 5256, 9900, 23562, 99540, 8190, 22940, 36290, 152490, 12210, 6314, 53592, 224202, 17556, 32580, 76452, 318660, 24492, 9702, 105950, 440232, 33306, 92008, 143262, 593670, 44310, 81510, 189660, 784110, 57840

Offset: 1

Author

M. F. Hasler, May 16 2015

Keywords

• nonn

Comments

See A073101 for more details.

This differs from A075247 starting with a(89) = 61410 vs. A075247(89) = 108936, corresponding to the representations 4/89 = 1/23 + 1/690 + 1/61410 = 1/24 + 1/306 + 1/108936.

Links

• M. F. Hasler, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A073101, A075245, A075246, A075247.

Programs

PARI

apply( {A257841(n, t)=for(x=n\4+1, 3*n\4, for(y=max(1\t=4/n-1/x, x)+1, ceil(2/t)-1, numerator(t-1/y)==1 && return(y/(t*y-1))))}, [1..99]) \\ improved by M. F. Hasler, Jul 03 2022