OFFSET
2,2
COMMENTS
a(n) = 1 if n is even and a(n) is even if n is odd.
a(n) = least m>0 such that n!+1+m and n-m are not relatively prime. - Clark Kimberling, Jul 21 2012
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 2..10000
A. Balog, P. Erdős and G. Tenenbaum, On Arithmetic Functions Involving Consecutive Divisors, In: Analytical Number Theory, pp. 77-90, Birkhäuser, Basel, 1990.
FORMULA
a(2n+1) = A060684(n).
EXAMPLE
For n=35, divisors={1,5,7,35}; differences={4,2,28}; a(35) = smallest difference = 2.
MAPLE
read("transforms") :
A060680 := proc(n)
sort(convert(numtheory[divisors](n), list)) ;
DIFF(%) ;
min(op(%)) ;
end proc:
seq(A060680(n), n=2..60) ; # R. J. Mathar, May 23 2018
MATHEMATICA
a[n_] := Min@@(Drop[d=Divisors[n], 1]-Drop[d, -1]);
(* Second program: *)
a[n_] := Min[Differences[Divisors[n]]];
Table[a[n], {n, 2, 100}] (* Jean-François Alcover, Oct 16 2024 *)
PROG
(Haskell)
a060680 = minimum . a193829_row -- Reinhard Zumkeller, Jun 25 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 19 2001
EXTENSIONS
Corrected by David W. Wilson, May 04 2001
Edited by Dean Hickerson, Jan 22 2002
STATUS
approved