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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.

%I A117553 #20 Mar 11 2021 17:01:22
%S A117553 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,
%T A117553 42,40,28,30,42,32,63,48,54,48,37,38,60,56,50,42,54,44,84,78,72,48,52,
%U A117553 57,93,72,98,54,66,72,64,80,90,60,78,62,96,104,127,84,78,68,126,96,74,72
%N 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.
%C A117553 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
%H A117553 Harvey P. Dale, <a href="/A117553/b117553.txt">Table of n, a(n) for n = 1..1000</a>
%e A117553 12's divisors are 1,2,3,4,6 and 12. Adding the divisors in order we have:
%e A117553 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.
%e A117553 Of these sums, 1+2+3+4+6 = 16 is the lowest which is >= 12. So a(12) = 16.
%p A117553 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
%t A117553 Table[Select[Accumulate[Divisors[n]],#>=n&,1],{n,80}]//Flatten (* _Harvey P. Dale_, Apr 05 2017 *)
%Y A117553 Cf. A117552, A125746, A125747.
%K A117553 nonn
%O A117553 1,2
%A A117553 _Leroy Quet_, Mar 28 2006
%E A117553 More terms from _R. J. Mathar_, Mar 14 2007