A333496 Least k of Egyptian fractions 1 = 1/x_1 + ... + 1/x_k , with 0 < x_1 <= ... <= x_k = n.

1, 2, 3, 3, 5, 3, 7, 4, 5, 4, 11, 4, 13, 5, 4, 5, 17, 4, 19, 4, 5, 7, 23, 4, 8, 8, 6, 5, 29, 5, 31, 6, 5, 10, 5, 5, 37

Offset

1,2

Links

Table of n, a(n) for n=1..37.

Index entries for sequences related to Egyptian fractions

Formula

a(n) <= n.

a(m * n) <= a(n) + m - 1.

If p is prime, a(p) = p.

If m is odd, a(2 * m) <= (m - 1)/2 + 2 because 1 = 1/2 + (m - 1)/2 * 1/m + 1/(2 * m).

Example

One of solutions
  n  |  [x_1, x_2, ... , x_a(n)]
-----+--------------------------------------
   4 | [2,  4,  4]
   6 | [2,  3,  6]
   8 | [2,  4,  8,  8]
   9 | [2,  6,  9,  9,  9]
  10 | [2,  5,  5, 10]
  12 | [2,  3, 12, 12]
  14 | [2,  7,  7,  7, 14]
  15 | [2,  3, 10, 15]
  16 | [2,  4,  8, 16, 16]
  18 | [2,  3,  9, 18]
  20 | [2,  4,  5, 20]
  21 | [2,  3, 14, 21, 21]
  22 | [2, 11, 11, 11, 11, 11, 22]
  24 | [2,  3,  8, 24]
  25 | [2,  4, 20, 25, 25, 25, 25, 25]
  26 | [2, 13, 13, 13, 13, 13, 13, 26]
  27 | [2,  3, 18, 27, 27, 27]
  28 | [2,  3, 12, 21, 28]
  30 | [2,  3, 10, 30, 30]
  32 | [2,  3, 16, 24, 32, 32]
  33 | [2,  3, 11, 22, 33]
  34 | [2, 17, 17, 17, 17, 17, 17, 17, 17, 34]
  35 | [2,  3, 14, 15, 35]
  36 | [2,  3,  9, 36, 36]

Crossrefs

Cf. A020473, A092666, A333437.

Sequence in context: A275940 A105555 A066858 * A152864 A152984 A177980

Adjacent sequences: A333493 A333494 A333495 * A333497 A333498 A333499

Keyword

nonn,more

Author

Seiichi Manyama, Mar 24 2020

Status

approved