cp's OEIS Frontend

A187795 Sum of the abundant divisors of n.

%I A187795 #43 Sep 22 2021 11:28:07
%S A187795 0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,18,0,20,0,0,0,36,0,0,0,0,0,30,0,0,
%T A187795 0,0,0,66,0,0,0,60,0,42,0,0,0,0,0,84,0,0,0,0,0,72,0,56,0,0,0,122,0,0,
%U A187795 0,0,0,66,0,0,0,70,0,162,0,0,0,0,0,78,0,140,0,0,0,138,0,0,0,88,0,138,0,0,0,0,0,180
%N A187795 Sum of the abundant divisors of n.
%C A187795 Sum of divisors d of n with sigma(d) > 2*d.
%C A187795 a(n) = n when n is a primitive abundant number (A091191). - _Alonso del Arte_, Jan 19 2013
%H A187795 Charles R Greathouse IV, <a href="/A187795/b187795.txt">Table of n, a(n) for n = 1..10000</a>
%H A187795 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%F A187795 From _Antti Karttunen_, Nov 14 2017: (Start)
%F A187795 a(n) = Sum_{d|n} A294937(d)*d.
%F A187795 a(n) = A294889(n) + (A294937(n)*n).
%F A187795 If A294889(n) > 0, then a(n) = A294889(n)+n, otherwise a(n) = A294930(n)*n.
%F A187795 a(n) + A187794(n) + A187793(n) = A000203(n).
%F A187795 (End)
%e A187795 a(12) = 12 because the divisors of 12 are 1, 2, 3, 4, 6, 12, but of those only 12 is abundant.
%e A187795 a(13) = 0 because the divisors of 13 are 1 and 13, neither of which is abundant.
%p A187795 A187795 := proc(n)
%p A187795     local a,d;
%p A187795     a :=0 ;
%p A187795     for d in numtheory[divisors](n) do
%p A187795         if numtheory[sigma](d) > 2* d then
%p A187795             a := a+d ;
%p A187795         end if;
%p A187795     end do:
%p A187795     return a;
%p A187795 end proc:
%p A187795 seq(A187795(n),n=1..100) ; # _R. J. Mathar_, Apr 27 2017
%t A187795 Table[Total@ Select[Divisors@ n, DivisorSigma[1, #] > 2 # &], {n, 96}] (* _Michael De Vlieger_, Jul 16 2016 *)
%o A187795 (PARI) a(n)=sumdiv(n,d,(sigma(d,-1)>2)*d) \\ _Charles R Greathouse IV_, Jan 15 2013
%o A187795 (Python)
%o A187795 from sympy import divisors, divisor_sigma
%o A187795 def A187795(n): return sum(d for d in divisors(n,generator=True) if divisor_sigma(d) > 2*d) # _Chai Wah Wu_, Sep 22 2021
%Y A187795 Cf. A000203, A005101, A080224, A270660, A271113, A294889, A294930, A294937.
%K A187795 nonn,easy
%O A187795 1,12
%A A187795 _Timothy L. Tiffin_, Jan 06 2013