A297053 - OEIS

%I #12 Feb 10 2018 22:00:33

%S 0,0,0,0,3,0,9,5,12,13,30,7,45,38,41,43,84,48,108,67,103,124,165,78,

%T 178,185,192,175,273,162,315,247,308,343,350,244,459,440,451,360,570,

%U 411,630,535,545,670,759,496,786,718,818,787,975,768,959,834,1042

%N Sum of the larger parts of the partitions of n into two parts such that the smaller part does not divide the larger.

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

%F a(n) = Sum_{i=1..floor(n/2)} (n-i) * (1 - (floor(n/i) - floor((n-1)/i))).

%e a(10) = 13; the partitions of 10 into two parts are (9,1), (8,2), (7,3), (6,4) and (5,5). The sum of the larger parts of these partitions such that the smaller part does not divide the larger is then 7 + 6 = 13.

%t Table[Sum[(n - i) (1 - (Floor[n/i] - Floor[(n - 1)/i])), {i, Floor[n/2]}], {n, 80}]

%Y Cf. A297024.

%K nonn,easy

%O 1,5

%A _Wesley Ivan Hurt_, Dec 24 2017