A350804 Numbers k with exactly one partition into two parts (s,t), s<=t, such that t | s*k.

2, 4, 8, 10, 14, 15, 16, 22, 26, 32, 34, 35, 38, 44, 46, 50, 52, 58, 62, 63, 64, 68, 74, 75, 76, 77, 82, 86, 91, 92, 94, 98, 99, 106, 116, 117, 118, 122, 124, 128, 134, 136, 142, 143, 146, 148, 152, 153, 158, 164, 166, 172, 175, 178, 184, 187, 188, 189, 194, 202, 206, 209

Offset: 1

Author

Wesley Ivan Hurt, Jan 16 2022

Keywords

• nonn

Comments

Numbers k such that k^2 has exactly one divisor d with k/2 <= d < k. - Robert Israel, Jan 08 2025

Examples

			15 is in the sequence since 15 = 6+9 has exactly one partition into two parts (6,9) such that 9 | 6*15 = 90.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to partitions

Crossrefs

Cf. A338021, A350803 (at least one).

Programs

Maple

filter:= proc(n) nops(select(t -> t >= n/2 and t < n, numtheory:-divisors(n^2)))=1 end proc:
select(filter, [$1..1000]); # Robert Israel, Jan 08 2025

PARI

f(n) = sum(s=1, n\2, !((s*n)%(n-s))); \\ A338021
isok(k) = f(k) == 1; \\ Michel Marcus, Jan 17 2022