OFFSET
1,2
COMMENTS
Sum of divisors d of n with sigma(d) < 2*d.
a(n) = sigma(n) when n is itself also deficient.
Also, a(n) agrees with the terms in A117553 except when n is a multiple (k > 1) of either a perfect number or a primitive abundant number.
Notice that a(1) = 1. The remaining fixed points are given by A125310. - Timothy L. Tiffin, Jun 23 2016
a(A028982(n)) is an odd integer. Also, if n is an odd abundant number that is not a perfect square and n has an odd number of abundant divisors (e.g., 945 has one abundant divisor and 4725 has three abundant divisors), then a(n) will also be odd: a(945) = 975 and a(4725) = 2675. - Timothy L. Tiffin, Jul 18 2016
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
a(12) = 10 because the divisors of 12 are 1, 2, 3, 4, 6, 12; of these, 1, 2, 3, 4 are deficient, and they add up to 10.
MAPLE
A187793 := 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:
a ;
end proc:# R. J. Mathar, May 08 2019
MATHEMATICA
Table[Total@ Select[Divisors@ n, DivisorSigma[1, #] < 2 # &], {n, 72}] (* Michael De Vlieger, Jul 18 2016 *)
PROG
(PARI) a(n)=sumdiv(n, d, if(sigma(d, -1)<2, d, 0)) \\ Charles R Greathouse IV, Jan 07 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Timothy L. Tiffin, Jan 06 2013
EXTENSIONS
a(54) corrected by Charles R Greathouse IV, Jan 07 2013
STATUS
approved