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

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to sums of divisors

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A117553, A109883.

Sequence in context: A076889 A134689 A248029 * A294886 A357698 A069250

Adjacent sequences: A117549 A117550 A117551 * A117553 A117554 A117555

Keyword

nonn

Author

Leroy Quet, Mar 28 2006

Extensions

More terms from Emeric Deutsch, Apr 01 2006

Status

approved