cp's OEIS Frontend

A238535 Sum of divisors d of n where d > sqrt(n).

%I A238535 #15 Mar 09 2014 15:08:58
%S A238535 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 A238535 39,36,49,29,61,31,56,44,51,42,75,37,57,52,78,41,84,43,77,69,69,47,
%U A238535 108,49,85,68,91,53,108,66,106,76,87,59,147,61,93,93,112,78,132
%N A238535 Sum of divisors d of n where d > sqrt(n).
%C A238535 Properties of the sequence:
%C A238535 a(n) = n if n is prime because sigma(n) = n+1 and A066839(n) = 1;
%C A238535 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 A238535 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 A238535 Michel Lagneau, <a href="/A238535/b238535.txt">Table of n, a(n) for n = 1..10000</a>
%F A238535 a(n) = A000203(n) - A066839(n).
%e A238535 a(8) = 12 because A000203(8)= 15 and A066839(8) = 3 => 15 - 8 = 12.
%t A238535 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 A238535 (PARI) a(n) = sumdiv(n, d, d*(d>sqrt(n))); \\ _Michel Marcus_, Feb 28 2014
%o A238535 (Sage)
%o A238535 def a(n):
%o A238535     return sum([d for d in Integer(n).divisors() if d>sqrt(n)]) # _Ralf Stephan_, Mar 08 2014
%Y A238535 Cf. A000203, A066839, A182147, A238502.
%K A238535 nonn
%O A238535 1,2
%A A238535 _Michel Lagneau_, Feb 28 2014
%E A238535 Better name from _Ralf Stephan_, Mar 08 2014