A117553 When adding some positive divisors of n in order from lowest divisor to highest divisor, a(n) is lowest sum achievable which is >= n.

1, 3, 4, 7, 6, 6, 8, 15, 13, 18, 12, 16, 14, 24, 24, 31, 18, 21, 20, 22, 32, 36, 24, 24, 31, 42, 40, 28, 30, 42, 32, 63, 48, 54, 48, 37, 38, 60, 56, 50, 42, 54, 44, 84, 78, 72, 48, 52, 57, 93, 72, 98, 54, 66, 72, 64, 80, 90, 60, 78, 62, 96, 104, 127, 84, 78, 68, 126, 96, 74, 72

Offset: 1

Author

Leroy Quet, Mar 28 2006

Keywords

• nonn

Comments

Often, but not always, a(n)=n+A054024(n). The exceptions to this rule are at n=24, 36, 48, 60, 72, 84,90, 96, 108, ... - R. J. Mathar, Mar 14 2007

Examples

			12's divisors are 1,2,3,4,6 and 12. Adding the divisors in order we have:
1 = 1, 1+2 = 3, 1+2+3 = 6, 1+2+3+4 = 10, 1+2+3+4+6 = 16 and 1+2+3+4+6+12 = 28.
Of these sums, 1+2+3+4+6 = 16 is the lowest which is >= 12. So a(12) = 16.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A117552, A125746, A125747.

Programs

Maple

A117553 := proc(n) local divs,a,i ; divs := numtheory[divisors](n) ; a := op(1,divs) ; i := 1 ; while a < n do i := i+1 ; a := a+op(i,divs) ; od ; RETURN(a) ; end: for n from 1 to 80 do printf("%d, ",A117553(n)) ; od ; # R. J. Mathar, Mar 14 2007

Mathematica

Table[Select[Accumulate[Divisors[n]],#>=n&,1],{n,80}]//Flatten (* Harvey P. Dale, Apr 05 2017 *)

Extensions

More terms from R. J. Mathar, Mar 14 2007