A350803 - OEIS

%I #26 Jan 26 2022 08:33:28

%S 2,4,6,8,10,12,14,15,16,18,20,22,24,26,28,30,32,34,35,36,38,40,42,44,

%T 45,46,48,50,52,54,56,58,60,62,63,64,66,68,70,72,74,75,76,77,78,80,82,

%U 84,86,88,90,91,92,94,96,98,99,100,102,104,105,106,108,110,112,114,116

%N Numbers k with at least one partition into two parts (s,t), s<=t such that t | s*k.

%C From _Bernard Schott_, Jan 22 2022: (Start)

%C A299174 is a subsequence because, if k = 2*u, we have s=t=u, s<=t, and u | u*k.

%C A082663 is another subsequence because, if k = p*q with p < q < 2p, then with s = k-p^2 = p*(q-p) and t = p^2, we have s <= t and p^2 | p*(q-p) * (pq).

%C It seems that A090196 is the subsequence of odd terms. (End)

%C gcd(s, t) > 1 where s and t and k > 2 are as in name. - _David A. Corneth_, Jan 22 2022

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%e 15 is in the sequence since 15 = 6+9 where 9 | 6*15 = 90.

%o (PARI) f(n) = sum(s=1, n\2, !((s*n)%(n-s))); \\ A338021

%o isok(k) = f(k) >= 1; \\ _Michel Marcus_, Jan 17 2022

%Y Cf. A338021, A350804 (exactly one).

%Y Subsequences: A082663, A299174.

%Y Cf. A090196.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, Jan 16 2022