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A181063 Smallest positive integer with a discrete string of exactly n consecutive divisors, or 0 if no such integer exists. 15
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 (list; graph; refs; listen; history; text; internal format)
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
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).
Sequence in context: A007668 A089415 A282974 * A161324 A226603 A116534
KEYWORD
nonn
AUTHOR
Matthew Vandermast, Oct 07 2010
STATUS
approved

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Last modified June 16 19:52 EDT 2024. Contains 373432 sequences. (Running on oeis4.)