A271113 -id:A271113 - cp's OEIS frontend

A187795 Sum of the abundant divisors of n.

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, 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, 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

Offset: 1

Timothy L. Tiffin, Jan 06 2013

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

a(n) = n when n is a primitive abundant number (A091191). - Alonso del Arte, Jan 19 2013

			a(12) = 12 because the divisors of 12 are 1, 2, 3, 4, 6, 12, but of those only 12 is abundant.
a(13) = 0 because the divisors of 13 are 1 and 13, neither of which is abundant.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sums of divisors

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

A187795 := proc(n)
    local a,d;
    a :=0 ;
    for d in numtheory[divisors](n) do
        if numtheory[sigma](d) > 2* d then
            a := a+d ;
        end if;
    end do:
    return a;
end proc:
seq(A187795(n),n=1..100) ; # R. J. Mathar, Apr 27 2017

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

a(n)=sumdiv(n,d,(sigma(d,-1)>2)*d) \\ Charles R Greathouse IV, Jan 15 2013

from sympy import divisors, divisor_sigma
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

From Antti Karttunen, Nov 14 2017: (Start)
a(n) = Sum_{d|n} A294937(d)*d.
a(n) = A294889(n) + (A294937(n)*n).
If A294889(n) > 0, then a(n) = A294889(n)+n, otherwise a(n) = A294930(n)*n.
a(n) + A187794(n) + A187793(n) = A000203(n).
(End)

A283550 Numbers that are not the sum of abundant numbers (not necessarily distinct).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 39, 41, 43, 45, 46, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107

Offset: 1

Amiram Eldar, Mar 10 2017

a(496) = 991 is the last term.
Subsequence of A048242 (Numbers that are not the sum of two abundant numbers).
Giovanni Resta noticed that 991 is the largest number that is not a sum of abundant numbers.

			20161 = 12 + 304 + 19845 is the sum of 3 abundant numbers and thus not in the sequence (although it is in A048242, since it is not the sum of 2 abundant numbers).

Amiram Eldar, Table of n, a(n) for n = 1..496
Giovanni Resta, abundant numbers

Cf. A271113, A048242, A005101.

AbundantQ[n_] := DivisorSigma[1, n] > 2 n; a = Select[Range[1000], AbundantQ[#] &]; nn = Dimensions[a][[1]]; t = Rest[CoefficientList[ Series[Product[(1 + x^a[[k]]), {k, nn}], {x, 0, a[[-1]]}], x]]; f = Flatten[Position[t, 0]]

cp's OEIS Frontend

A187795 Sum of the abundant divisors of n.

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