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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
OFFSET
1,19
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.
Sequence in context: A085075 A321518 A267883 * A058257 A330959 A083199
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Mar 24 2020
STATUS
approved