OFFSET
1,10
COMMENTS
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
William G. Stanton and Judy A. Holdener, Abundancy "Outlaws" of the Form (sigma(N) + t)/N, Journal of Integer Sequences , Vol 10 (2007) , Article 07.9.6.
EXAMPLE
For n=10, sigma(10)/10 = 18/10 = 9/5 = (sigma(5) + 3)/5, hence a(10)=3.
MAPLE
with(numtheory): A240923:=n->numer(sigma(n)/n) - sigma(denom(sigma(n)/n)): seq(A240923(n), n=1..100); # Wesley Ivan Hurt, Aug 06 2014
MATHEMATICA
Table[Numerator[DivisorSigma[1, n]/n] - DivisorSigma[1, Denominator[ DivisorSigma[1, n]/n]], {n, 100}] (* Wesley Ivan Hurt, Aug 06 2014 *)
PROG
(PARI) a(n) = my(ab = sigma(n)/n); numerator(ab) - sigma(denominator(ab));
(Haskell)
import Data.Ratio ((%), numerator, denominator)
a240923 n = numerator sq - a000203 (denominator sq)
where sq = a000203 n % n
-- Reinhard Zumkeller, Aug 05 2014
(Python)
from gmpy2 import mpq
from sympy import divisors
map(lambda x: x.numerator-sum(divisors(x.denominator)), [mpq(sum(divisors(n)), n) for n in range(1, 10**5)]) # Chai Wah Wu, Aug 05 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Aug 03 2014
STATUS
approved