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A060680 Smallest difference between consecutive divisors of n. 38
1, 2, 1, 4, 1, 6, 1, 2, 1, 10, 1, 12, 1, 2, 1, 16, 1, 18, 1, 2, 1, 22, 1, 4, 1, 2, 1, 28, 1, 30, 1, 2, 1, 2, 1, 36, 1, 2, 1, 40, 1, 42, 1, 2, 1, 46, 1, 6, 1, 2, 1, 52, 1, 4, 1, 2, 1, 58, 1, 60, 1, 2, 1, 4, 1, 66, 1, 2, 1, 70, 1, 72, 1, 2, 1, 4, 1, 78, 1, 2, 1, 82, 1, 4, 1, 2, 1, 88, 1, 6, 1, 2, 1, 4 (list; graph; refs; listen; history; text; internal format)
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
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])
PROG
(Haskell)
a060680 = minimum . a193829_row -- Reinhard Zumkeller, Jun 25 2015
CROSSREFS
Cf. A060681 (largest difference), A060682, A060683, A060684.
Sequence in context: A256908 A346466 A258409 * A057237 A187730 A049559
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

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)