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

1,12

Comments

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sums of divisors

Formula

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)

Example

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.

Maple

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A063863 A236238 A340362 * A101364 A216809 A204274

Adjacent sequences: A187792 A187793 A187794 * A187796 A187797 A187798

Keyword

nonn,easy

Author

Timothy L. Tiffin, Jan 06 2013

Status

approved