A117552 Largest partial sum of the increasingly ordered divisors of n, not exceeding n.

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, 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, 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

Offset: 1

Author

Leroy Quet, Mar 28 2006

Keywords

• nonn

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to sums of divisors

Crossrefs

Cf. A117553, A109883, A377247 (corresponding largest divisor index).

Programs

Maple

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

Mathematica

Table[Last@ TakeWhile[Accumulate@ Divisors@ n, # <= n &], {n, 80}] (* Michael De Vlieger, Oct 30 2017 *)

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

Formula

a(n) = n - A109883(n). - Ridouane Oudra, Jan 25 2024

Extensions

More terms from Emeric Deutsch, Apr 01 2006