This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049798 #81 Oct 20 2023 21:13:23
%S A049798 0,0,0,1,0,2,2,2,3,7,2,7,10,8,8,15,11,19,16,15,22,32,19,25,34,34,33,
%T A049798 46,33,47,47,48,61,65,45,62,77,79,68,87,74,94,97,86,105,127,98,114,
%U A049798 120,124,129,154,141,151,142,147,172,200,151,180
%N A049798 a(n) = (1/2)*Sum_{k = 1..n} T(n,k), array T as in A049800.
%C A049798 a(n) is the sum of the remainders after dividing each larger part by its corresponding smaller part for each partition of n+1 into two parts. - _Wesley Ivan Hurt_, Dec 20 2020
%H A049798 Lei Zhou, <a href="/A049798/b049798.txt">Table of n, a(n) for n = 1..10000</a>
%F A049798 a(n) = Sum_{k=2..floor((n+1)/2)} ((n+1) mod k). - _Lei Zhou_, Mar 10 2014
%F A049798 a(n) = A004125(n+1) - A008805(n-2), for n >= 2. - _Carl Najafi_, Jan 31 2013
%F A049798 a(n) = Sum_{i = 1..ceiling(n/2)} ((n-i+1) mod i). - _Wesley Ivan Hurt_, Jan 05 2017
%e A049798 From _Lei Zhou_, Mar 10 2014: (Start)
%e A049798 For n = 3, n+1 = 4, floor((n+1)/2) = 2, mod(4,2) = 0, and so a(3) = 0.
%e A049798 For n = 4, n+1 = 5, floor((n+1)/2) = 2, mod(5,2) = 1, and so a(4) = 1.
%e A049798 ...
%e A049798 For n = 12, n+1 = 13, floor((n+1)/2) = 6, mod(13,2) = 1, mod(13,3) = 1, mod(13,4) = 1, mod(13,5) = 3, mod(13,6) = 1, and so a(12) = 1 + 1 + 1 + 3 + 1 = 7. (End)
%p A049798 seq( add( (n+1) mod floor((k+1)/2), k=1..n)/2, n=1..60); # _G. C. Greubel_, Dec 09 2019
%t A049798 Table[Sum[Mod[n+1, Floor[(k+1)/2]], {k,n}]/2, {n, 60}] (* _G. C. Greubel_, Dec 09 2019 *)
%o A049798 (Sage)
%o A049798 def a(n):
%o A049798 return sum([(n+1)%k for k in range(2,floor((n+3)/2))])
%o A049798 # _Ralf Stephan_, Mar 14 2014
%o A049798 (PARI) vector(60, n, sum(k=1,n, lift(Mod(n+1, (k+1)\2)) )/2 ) \\ _G. C. Greubel_, Dec 09 2019
%o A049798 (Magma) [ (&+[(n+1) mod Floor((k+1)/2): k in [1..n]])/2: n in [1..60]]; // _G. C. Greubel_, Dec 09 2019
%o A049798 (GAP) List([1..60], n-> Sum([1..n], k-> (n+1) mod Int((k+1)/2))/2 ); # _G. C. Greubel_, Dec 09 2019
%o A049798 (Python)
%o A049798 def A049798(n): return sum((n+1)%k for k in range(2,(n+1>>1)+1)) # _Chai Wah Wu_, Oct 20 2023
%Y A049798 Cf. A004125, A008611, A008805, A049797, A049799, A049801.
%Y A049798 Half row sums of A049800.
%K A049798 nonn,easy
%O A049798 1,6
%A A049798 _Clark Kimberling_