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 A117552 #24 Aug 05 2025 13:35:32
%S A117552 1,1,1,3,1,6,1,7,4,8,1,10,1,10,9,15,1,12,1,12,11,14,1,24,6,16,13,28,1,
%T A117552 27,1,31,15,20,13,25,1,22,17,30,1,33,1,40,33,26,1,36,8,43,21,46,1,39,
%U A117552 17,36,23,32,1,58,1,34,41,63,19,45,1,58,27,39,1,63,1,40,49,64,19,51,1,66
%N A117552 Largest partial sum of the increasingly ordered divisors of n, not exceeding n.
%H A117552 Antti Karttunen, <a href="/A117552/b117552.txt">Table of n, a(n) for n = 1..16384</a>
%H A117552 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%F A117552 a(n) = n - A109883(n). - _Ridouane Oudra_, Jan 25 2024
%e A117552 a(12)=10 because the increasingly ordered divisors of 12 are 1,2,3,4,6 and 12, with partial sums 1,3,6,10,16 and 28; the largest partial sum not exceeding 12 is 10.
%p A117552 with(numtheory): a:=proc(n) local div,j: if n=1 then 1 else div:=divisors(n): for j from 1 by 1 while sum(div[i],i=1..j)<=n do sum(div[k],k=1..j) od: fi: end: seq(a(n),n=1..90); # _Emeric Deutsch_, Apr 01 2006
%t A117552 Table[Last@ TakeWhile[Accumulate@ Divisors@ n, # <= n &], {n, 80}] (* _Michael De Vlieger_, Oct 30 2017 *)
%o A117552 (PARI) A117552(n) = { my(divs=divisors(n), s=0); for(i=1,#divs,if((s+divs[i])>n,return(s),s+=divs[i])); s; }; \\ _Antti Karttunen_, Oct 30 2017
%Y A117552 Cf. A117553, A109883, A377247 (corresponding largest divisor index).
%K A117552 nonn
%O A117552 1,4
%A A117552 _Leroy Quet_, Mar 28 2006
%E A117552 More terms from _Emeric Deutsch_, Apr 01 2006