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A187795 Sum of the abundant divisors of n. 16
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A063863 A236238 A340362 * A101364 A216809 A204274
KEYWORD
nonn,easy
AUTHOR
Timothy L. Tiffin, Jan 06 2013
STATUS
approved

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Last modified May 18 01:50 EDT 2024. Contains 372614 sequences. (Running on oeis4.)