|
%I #61 May 08 2019 13:34:45
%S 1,3,4,7,6,6,8,15,13,18,12,10,14,24,24,31,18,15,20,22,32,36,24,18,31,
%T 42,40,28,30,36,32,63,48,54,48,19,38,60,56,30,42,48,44,84,78,72,48,34,
%U 57,93,72,98,54,42,72,36,80,90,60,40,62,96,104,127,84,72,68,126,96,74,72,27
%N Sum of the deficient divisors of n.
%C Sum of divisors d of n with sigma(d) < 2*d.
%C a(n) = sigma(n) when n is itself also deficient.
%C Also, a(n) agrees with the terms in A117553 except when n is a multiple (k > 1) of either a perfect number or a primitive abundant number.
%C Notice that a(1) = 1. The remaining fixed points are given by A125310. - _Timothy L. Tiffin_, Jun 23 2016
%C a(A028982(n)) is an odd integer. Also, if n is an odd abundant number that is not a perfect square and n has an odd number of abundant divisors (e.g., 945 has one abundant divisor and 4725 has three abundant divisors), then a(n) will also be odd: a(945) = 975 and a(4725) = 2675. - _Timothy L. Tiffin_, Jul 18 2016
%H Charles R Greathouse IV, <a href="/A187793/b187793.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%F From _Antti Karttunen_, Nov 14 2017: (Start)
%F a(n) = Sum_{d|n} A294934(d)*d.
%F a(n) = A294886(n) + (A294934(n)*n).
%F a(n) + A187794(n) + A187795(n) = A000203(n).
%F (End)
%e a(12) = 10 because the divisors of 12 are 1, 2, 3, 4, 6, 12; of these, 1, 2, 3, 4 are deficient, and they add up to 10.
%p A187793 := proc(n)
%p local a,d ;
%p a := 0 ;
%p for d in numtheory[divisors](n) do
%p if numtheory[sigma](d) < 2*d then
%p a := a+d ;
%p end if ;
%p end do:
%p a ;
%p end proc:# _R. J. Mathar_, May 08 2019
%t Table[Total@ Select[Divisors@ n, DivisorSigma[1, #] < 2 # &], {n, 72}] (* _Michael De Vlieger_, Jul 18 2016 *)
%o (PARI) a(n)=sumdiv(n,d,if(sigma(d,-1)<2,d,0)) \\ _Charles R Greathouse IV_, Jan 07 2013
%Y Cf. A000203, A005100, A028982, A080226, A117553, A125310, A125499, A187794, A187795, A247328, A274338, A274339, A274340, A274380, A274549, A274829, A294886, A294934.
%K nonn,easy
%O 1,2
%A _Timothy L. Tiffin_, Jan 06 2013
%E a(54) corrected by _Charles R Greathouse IV_, Jan 07 2013
|
