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Sum of divisors d of n where d > sqrt(n).
35

%I #15 Mar 09 2014 15:08:58

%S 0,2,3,4,5,9,7,12,9,15,11,22,13,21,20,24,17,33,19,35,28,33,23,50,25,

%T 39,36,49,29,61,31,56,44,51,42,75,37,57,52,78,41,84,43,77,69,69,47,

%U 108,49,85,68,91,53,108,66,106,76,87,59,147,61,93,93,112,78,132

%N Sum of divisors d of n where d > sqrt(n).

%C Properties of the sequence:

%C a(n) = n if n is prime because sigma(n) = n+1 and A066839(n) = 1;

%C a(p^2) = p^2 if p is prime because sigma(p^2) = p^2+p+1 and A066839(p^2)= p+1 => A000203(p^2) - A066839(p^2)= p^2;

%C a(m) = 2*m if m = A182147(n) = 42, 54, 66, 78, 102, 114,... (numbers n equal to the sum of its proper divisors greater than square root of n).

%H Michel Lagneau, <a href="/A238535/b238535.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000203(n) - A066839(n).

%e a(8) = 12 because A000203(8)= 15 and A066839(8) = 3 => 15 - 8 = 12.

%t lst={}; f[n_]:=DivisorSigma[1,n]-Plus@@Select[Divisors@n,#<=Sqrt@n&];Do[If[IntegerQ[f[n]],AppendTo[lst, f[n]]],{n,1,200}];lst

%o (PARI) a(n) = sumdiv(n, d, d*(d>sqrt(n))); \\ _Michel Marcus_, Feb 28 2014

%o (Sage)

%o def a(n):

%o return sum([d for d in Integer(n).divisors() if d>sqrt(n)]) # _Ralf Stephan_, Mar 08 2014

%Y Cf. A000203, A066839, A182147, A238502.

%K nonn

%O 1,2

%A _Michel Lagneau_, Feb 28 2014

%E Better name from _Ralf Stephan_, Mar 08 2014