A181063 Smallest positive integer with a discrete string of exactly n consecutive divisors, or 0 if no such integer exists.

1, 2, 6, 12, 3960, 60, 420, 840, 17907120, 2520, 411863760, 27720, 68502634200, 447069823200, 360360, 720720, 7600186994400, 12252240, 9524356075634400, 81909462250455840, 1149071006394511200, 232792560, 35621201198229847200, 5354228880, 91351145008363640400

Offset

1,2

Comments

The word "discrete" is used to describe a string of consecutive divisors that is not part of a longer such string.

Does a(n) ever equal 0?

a(n) = A003418(n) iff n belongs to A181062; otherwise, a(n) > A003418(n). a(A181062(n)) = A051451(n).

Links

David W. Wilson, Table of n, a(n) for n = 1..1000

Example

a(5) = 3960 is divisible by 8, 9, 10, 11, and 12, but not 7 or 13. It is the smallest positive integer with a string of 5 consecutive divisors that is not part of a longer string.
From Gus Wiseman, Oct 16 2019: (Start)
The sequence of terms together with their divisors begins:
     1: {1}
     2: {1,2}
     6: {1,2,3,6}
    12: {1,2,3,4,6,12}
  3960: {1,2,...,8,9,10,11,12,...,1980,3960}
    60: {1,2,3,4,5,6,...,30,60}
   420: {1,2,3,4,5,6,7,...,210,420}
   840: {1,2,3,4,5,6,7,8,...,420,840}
(End)

Mathematica

tav=Table[Length/@Split[Divisors[n], #2==#1+1&], {n, 10000}];
Table[Position[tav, i][[1, 1]], {i, Split[Union@@tav, #2==#1+1&][[1]]}] (* Assumes there are no zeros. - Gus Wiseman, Oct 16 2019 *)

Crossrefs

The version taking only the longest run is A328449.

The longest run of divisors of n has length A055874(n).

Numbers whose divisors > 1 have no non-singleton runs are A088725.

The number of successive pairs of divisors of n is A129308(n).

Cf. A000005, A003418, A027750, A060775, A181064, A199970, A328166, A328448.

Sequence in context: A007668 A089415 A282974 * A161324 A226603 A116534

Adjacent sequences: A181060 A181061 A181062 * A181064 A181065 A181066

Keyword

nonn

Author

Matthew Vandermast, Oct 07 2010

Status

approved