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A060680 Smallest difference between consecutive divisors of n. 13
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

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, Birkhauser, 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.

Cf. A193829, A027750.

Sequence in context: A281071 A256908 A258409 * A057237 A187730 A049559

Adjacent sequences:  A060677 A060678 A060679 * A060681 A060682 A060683

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 April 24 04:00 EDT 2019. Contains 322406 sequences. (Running on oeis4.)