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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

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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 * A378385 A380263 A058257

Adjacent sequences: A333434 A333435 A333436 * A333438 A333439 A333440

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Mar 24 2020

STATUS

approved

URL: https://oeis.org/A333437

⇱ A333437 - OEIS