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
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
KEYWORD
nonn,easy
AUTHOR
Timothy L. Tiffin, Jan 06 2013
STATUS
approved