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

%I A350804 #18 Jan 08 2025 11:52:45
%S A350804 2,4,8,10,14,15,16,22,26,32,34,35,38,44,46,50,52,58,62,63,64,68,74,75,
%T A350804 76,77,82,86,91,92,94,98,99,106,116,117,118,122,124,128,134,136,142,
%U A350804 143,146,148,152,153,158,164,166,172,175,178,184,187,188,189,194,202,206,209
%N A350804 Numbers k with exactly one partition into two parts (s,t), s<=t, such that t | s*k.
%C A350804 Numbers k such that k^2 has exactly one divisor d with k/2 <= d < k. - _Robert Israel_, Jan 08 2025
%H A350804 Robert Israel, <a href="/A350804/b350804.txt">Table of n, a(n) for n = 1..10000</a>
%H A350804 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%e A350804 15 is in the sequence since 15 = 6+9 has exactly one partition into two parts (6,9) such that 9 | 6*15 = 90.
%p A350804 filter:= proc(n) nops(select(t -> t >= n/2 and t < n, numtheory:-divisors(n^2)))=1 end proc:
%p A350804 select(filter, [$1..1000]); # _Robert Israel_, Jan 08 2025
%o A350804 (PARI) f(n) = sum(s=1, n\2, !((s*n)%(n-s))); \\ A338021
%o A350804 isok(k) = f(k) == 1; \\ _Michel Marcus_, Jan 17 2022
%Y A350804 Cf. A338021, A350803 (at least one).
%K A350804 nonn
%O A350804 1,1
%A A350804 _Wesley Ivan Hurt_, Jan 16 2022