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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
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified January 20 10:09 EST 2022. Contains 350471 sequences. (Running on oeis4.)