A333437 Triangle read by rows: T(n,k) is the number of Egyptian fractions 1 = 1/x_1 + ... + 1/x_k , with 0 < x_1 <= ... <= x_k = n.

1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 3, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 3, 3, 2, 1, 0, 0, 0, 0, 2, 2, 3, 2, 1, 0, 0, 0, 1, 3, 6, 7, 5, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 8, 15, 21, 24, 20, 11, 4, 1

Offset

1,19

Links

Table of n, a(n) for n=1..78.

Index entries for sequences related to Egyptian fractions

Formula

T(n,n) = 1.

If n is prime, T(n,k) = 0 for 1 <= k < n.

Example

1 = 1/2 + 1/6 + 1/6 + 1/6 = 1/3 + 1/3 + 1/6 + 1/6 = 1/3 + 1/4 + 1/4 + 1/6. So T(6,4) = 3.
Triangle begins:
n\k  | 1  2  3  4  5   6   7   8   9  10 11 12
-----+----------------------------------------
   1 | 1;
   2 | 0, 1;
   3 | 0, 0, 1;
   4 | 0, 0, 1, 1;
   5 | 0, 0, 0, 0, 1;
   6 | 0, 0, 1, 3, 2,  1;
   7 | 0, 0, 0, 0, 0,  0,  1;
   8 | 0, 0, 0, 1, 3,  3,  2,  1;
   9 | 0, 0, 0, 0, 2,  2,  3,  2,  1;
  10 | 0, 0, 0, 1, 3,  6,  7,  5,  3,  1;
  11 | 0, 0, 0, 0, 0,  0,  0,  0,  0,  0, 1;
  12 | 0, 0, 0, 3, 8, 15, 21, 24, 20, 11, 4, 1;

Crossrefs

Row sums give A092666.

Cf. A020473, A333496.

Sequence in context: A085075 A321518 A267883 * A058257 A330959 A083199

Adjacent sequences: A333434 A333435 A333436 * A333438 A333439 A333440

Keyword

nonn,tabl

Author

Seiichi Manyama, Mar 24 2020

Status

approved