A385202 Irregular triangle read by rows: let S be an ordered set of nondivisors of n such that a and b belong to S if a + b = n. T(n,k) is the k-th member of S. If S is empty, T(n,k) = 0.

0, 0, 0, 0, 2, 3, 0, 2, 3, 4, 5, 3, 5, 2, 4, 5, 7, 3, 4, 6, 7, 2, 3, 4, 5, 6, 7, 8, 9, 5, 7, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 6, 8, 9, 10, 11, 2, 4, 6, 7, 8, 9, 11, 13, 3, 5, 6, 7, 9, 10, 11, 13, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 4, 5, 7, 8, 10, 11, 13, 14

Offset: 1

Author

Miles Englezou, Jun 21 2025

Keywords

• nonn
• tabf

Examples

			 n | Triangle begins:
---+-----------------
 1 | {}
 2 | {}
 3 | {}
 4 | {}
 5 | {2, 3}
 6 | {}
 7 | {2, 3, 4, 5}
 8 | {3, 5}
 9 | {2, 4, 5, 7}
10 | {3, 4, 6, 7}
11 | {2, 3, 4, 5, 6, 7, 8, 9}
12 | {5, 7}
13 | {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
14 | {3, 4, 5, 6, 8, 9, 10, 11}
15 | {2, 4, 6, 7, 8, 9, 11, 13}
16 | {3, 5, 6, 7, 9, 10, 11, 13}
17 | {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
18 | {4, 5, 7, 8, 10, 11, 13, 14}
19 | {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}
20 | {3, 6, 7, 8, 9, 11, 12, 13, 14, 17}
21 | {2, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 19}
22 | {3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19}
23 | {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21}
24 | {5, 7, 9, 10, 11, 13, 14, 15, 17, 19}
25 | {2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23}
		

Crossrefs

Cf. A086369.

Programs

PARI

T(n,k) = my(S); S = select(x -> setsearch(divisors(n), x)==0 && setsearch(divisors(n), n-x)==0, [1..n]); if(k <= #S, S[k], 0) \\ function made to output 0 if k exceeds the size of S to avoid breaking

Formula

n = T(n, m) + T(n, k-(m-1)), 1 <= m <= k, for every row of length k.

S defined as in the name, n - |S| = A086369(n).