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A126800
Smallest divisor of n which is greater than largest divisor d of n such that each integer from 1 to d is also a divisor of n.
3
3, 4, 5, 6, 7, 4, 3, 5, 11, 6, 13, 7, 3, 4, 17, 6, 19, 4, 3, 11, 23, 6, 5, 13, 3, 4, 29, 5, 31, 4, 3, 17, 5, 6, 37, 19, 3, 4, 41, 6, 43, 4, 3, 23, 47, 6, 7, 5, 3, 4, 53, 6, 5, 4, 3, 29, 59, 10, 61, 31, 3, 4, 5, 6, 67, 4, 3, 5, 71, 6, 73, 37, 3, 4, 7, 6, 79, 4
OFFSET
3,1
COMMENTS
a(n) is the smallest divisor of n which is greater than A055874(n).
a(n) is also the smallest divisor m, m > 1, of n where m - 1 is not a divisor of n.
LINKS
FORMULA
a(n) = n if n is an odd prime or if n = 4 or 6. - Alonso del Arte, Aug 07 2014
EXAMPLE
The divisors of 12 are 1, 2, 3, 4, 6, 12. The first four divisors are the first four positive integers, but 5 is not a divisor of 12, and the smallest divisor greater than 5 is 6, so a(12) = 6.
The divisors of 14 are 1, 2, 7, 14. The first two divisors are the first two positive integers, but 3 is not a divisor of 14, and the smallest divisor greater than 3 is 7, so a(14) = 7.
MAPLE
A055874 := proc(n) local m; for m from 1 do if n mod m <> 0 then RETURN(m-1) ; fi ; od: end: A126800 := proc(n) local a; for a from A055874(n)+1 do if n mod a = 0 then RETURN(a) ; fi ; od: end: seq(A126800(n), n=3..80) ; # R. J. Mathar, Nov 01 2007
MATHEMATICA
sdn[n_]:=Module[{divs=Divisors[n], s, c}, s=First[Split[Differences[divs]]]; c=Length[s]+1; Which[PrimeQ[n], n, First[s]>1, divs[[2]], True, First[Drop[ divs, c]]]]; Array[sdn, 80, 3] (* Harvey P. Dale, Jan 18 2015 *)
Array[#[[1 + LengthWhile[Prepend[Differences@ #, 1], # == 1 &] ]] &@ Divisors@ # &, 78, 3] (* Michael De Vlieger, Oct 10 2017 *)
CROSSREFS
Cf. A055874.
Sequence in context: A159077 A049267 A111608 * A245689 A182258 A067628
KEYWORD
nonn
AUTHOR
Leroy Quet, Feb 21 2007
EXTENSIONS
More terms from R. J. Mathar, Nov 01 2007
STATUS
approved