A187795 - OEIS

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

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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