A241883 Number of ways 1/n can be expressed as the sum of four distinct unit fractions: 1/n = 1/w + 1/x + 1/y + 1/z satisfying 0 < w < x < y < z.

6, 71, 272, 586, 978, 1591, 1865, 3115, 3772, 4964, 4225, 8433, 4987, 10667, 13659, 10845, 7513, 17360, 9569, 28554, 23309, 17220, 12326, 37554, 19984, 24091, 31056, 42343, 16095, 57001, 15076, 42655, 46885, 38416, 77887, 71959, 16692, 42054, 68894, 95914, 24566, 100023, 24224, 99437, 108756, 41907, 29711, 127069, 52811, 94745, 83433

Offset

1,1

Links

Jud McCranie, Table of n, a(n) for n = 1..644

Example

1/1 = 1/2 + 1/3 + 1/7  + 1/42
    = 1/2 + 1/3 + 1/8  + 1/24
    = 1/2 + 1/3 + 1/9  + 1/18
    = 1/2 + 1/3 + 1/10 + 1/15
    = 1/2 + 1/4 + 1/5  + 1/20
    = 1/2 + 1/4 + 1/6  + 1/12
so a(1) = 6.

Mathematica

a[n_] := Length@ Solve[1/n == 1/w + 1/x + 1/y + 1/z && 0 < w < x < y < z, {w, x, y, z}, Integers]; Array[f, 21]

Crossrefs

Cf. A002966, A004194, A020327, A227610.

Sequence in context: A211036 A284215 A050788 * A297746 A027317 A283342

Adjacent sequences: A241880 A241881 A241882 * A241884 A241885 A241886

Keyword

nonn

Author

Robert G. Wilson v, Apr 30 2014

Status

approved