A187795 - OEIS

%I #43 Sep 22 2021 11:28:07

%S 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 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 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 Sum of the abundant divisors of n.

%C Sum of divisors d of n with sigma(d) > 2*d.

%C a(n) = n when n is a primitive abundant number (A091191). - _Alonso del Arte_, Jan 19 2013

%H Charles R Greathouse IV, <a href="/A187795/b187795.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} A294937(d)*d.

%F a(n) = A294889(n) + (A294937(n)*n).

%F If A294889(n) > 0, then a(n) = A294889(n)+n, otherwise a(n) = A294930(n)*n.

%F a(n) + A187794(n) + A187793(n) = A000203(n).

%F (End)

%e a(12) = 12 because the divisors of 12 are 1, 2, 3, 4, 6, 12, but of those only 12 is abundant.

%e a(13) = 0 because the divisors of 13 are 1 and 13, neither of which is abundant.

%p A187795 := 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     return a;

%p end proc:

%p seq(A187795(n),n=1..100) ; # _R. J. Mathar_, Apr 27 2017

%t Table[Total@ Select[Divisors@ n, DivisorSigma[1, #] > 2 # &], {n, 96}] (* _Michael De Vlieger_, Jul 16 2016 *)

%o (PARI) a(n)=sumdiv(n,d,(sigma(d,-1)>2)*d) \\ _Charles R Greathouse IV_, Jan 15 2013

%o (Python)

%o from sympy import divisors, divisor_sigma

%o 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 Cf. A000203, A005101, A080224, A270660, A271113, A294889, A294930, A294937.

%K nonn,easy

%O 1,12

%A _Timothy L. Tiffin_, Jan 06 2013