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 A060681 Largest difference between consecutive divisors of n (ordered by size). 61
 0, 1, 2, 2, 4, 3, 6, 4, 6, 5, 10, 6, 12, 7, 10, 8, 16, 9, 18, 10, 14, 11, 22, 12, 20, 13, 18, 14, 28, 15, 30, 16, 22, 17, 28, 18, 36, 19, 26, 20, 40, 21, 42, 22, 30, 23, 46, 24, 42, 25, 34, 26, 52, 27, 44, 28, 38, 29, 58, 30, 60, 31, 42, 32, 52, 33, 66, 34, 46, 35, 70, 36, 72, 37 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Is a(n) the least m > 0 such that n - m divides n! + m? - Clark Kimberling, Jul 28 2012 Is a(n) the least m > 0 such that L(n-m) divides L(n+m), where L = A000032 (Lucas numbers)? - Clark Kimberling, Jul 30 2012 Records give A006093. - Omar E. Pol, Oct 26 2013 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..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(n) = n - n/A020639(n). a(n) = n - A032742(n). - Omar E. Pol, Aug 31 2011 EXAMPLE For n = 35, divisors are {1, 5, 7, 35}; differences are {4, 2, 28}; a(35) = largest difference = 28 = 35 - 35/5. MAPLE read("transforms") : A060681 := proc(n)     if n = 1 then         0 ;     else         sort(convert(numtheory[divisors](n), list)) ;         DIFF(%) ;         max(op(%)) ;     end if; end proc: seq(A060681(n), n=1..60) ; # R. J. Mathar, May 23 2018 MATHEMATICA a[n_ ] := n - n/FactorInteger[n][[1, 1]] Array[Max[Differences[Divisors[#]]] &, 80, 2] (* Harvey P. Dale, Oct 26 2013 *) PROG (Haskell) a060681 n = div n p * (p - 1) where p = a020639 n -- Reinhard Zumkeller, Apr 06 2015 (PARI) diff(v)=vector(#v-1, i, v[i+1]-v[i]) a(n)=vecmax(diff(divisors(n))) \\ Charles R Greathouse IV, Sep 02 2015 (PARI) a(n) = if (n==1, 0, n - n/factor(n)[1, 1]); \\ Michel Marcus, Oct 24 2015 (PARI) first(n) = n = max(n, 1); my(res = vector(n)); res = 0; forprime(p = 2, n, for(i = 1, n \ p, if(res[p * i] == 0, res[p * i] = i*(p-1)))); res \\ David A. Corneth, Jan 08 2019 CROSSREFS Cf. A020639, A060680, A060682, A060683, A060685, A171462. Sequence in context: A067240 A126080 A302043 * A202479 A161660 A343327 Adjacent sequences:  A060678 A060679 A060680 * A060682 A060683 A060684 KEYWORD nonn,easy AUTHOR Labos Elemer, Apr 19 2001 EXTENSIONS Edited by Dean Hickerson, Jan 22 2002 a(1)=0 added by N. J. A. Sloane, Oct 01 2015 at the suggestion of Antti Karttunen STATUS approved

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Last modified July 23 14:38 EDT 2021. Contains 346259 sequences. (Running on oeis4.)