OFFSET
1,2
COMMENTS
Properties of the sequence:
a(n) = n if n is prime because sigma(n) = n+1 and A066839(n) = 1;
a(p^2) = p^2 if p is prime because sigma(p^2) = p^2+p+1 and A066839(p^2)= p+1 => A000203(p^2) - A066839(p^2)= p^2;
a(m) = 2*m if m = A182147(n) = 42, 54, 66, 78, 102, 114,... (numbers n equal to the sum of its proper divisors greater than square root of n).
LINKS
Michel Lagneau, Table of n, a(n) for n = 1..10000
MATHEMATICA
lst={}; f[n_]:=DivisorSigma[1, n]-Plus@@Select[Divisors@n, #<=Sqrt@n&]; Do[If[IntegerQ[f[n]], AppendTo[lst, f[n]]], {n, 1, 200}]; lst
PROG
(PARI) a(n) = sumdiv(n, d, d*(d>sqrt(n))); \\ Michel Marcus, Feb 28 2014
(Sage)
def a(n):
return sum([d for d in Integer(n).divisors() if d>sqrt(n)]) # Ralf Stephan, Mar 08 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 28 2014
EXTENSIONS
Better name from Ralf Stephan, Mar 08 2014
STATUS
approved