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%I #19 Oct 19 2019 21:24:48
%S 1,2,6,12,3960,60,420,840,17907120,2520,411863760,27720,68502634200,
%T 447069823200,360360,720720,7600186994400,12252240,9524356075634400,
%U 81909462250455840,1149071006394511200,232792560,35621201198229847200,5354228880,91351145008363640400
%N Smallest positive integer with a discrete string of exactly n consecutive divisors, or 0 if no such integer exists.
%C The word "discrete" is used to describe a string of consecutive divisors that is not part of a longer such string.
%C Does a(n) ever equal 0?
%C a(n) = A003418(n) iff n belongs to A181062; otherwise, a(n) > A003418(n). a(A181062(n)) = A051451(n).
%H David W. Wilson, <a href="/A181063/b181063.txt">Table of n, a(n) for n = 1..1000</a>
%e 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.
%e From _Gus Wiseman_, Oct 16 2019: (Start)
%e The sequence of terms together with their divisors begins:
%e 1: {1}
%e 2: {1,2}
%e 6: {1,2,3,6}
%e 12: {1,2,3,4,6,12}
%e 3960: {1,2,...,8,9,10,11,12,...,1980,3960}
%e 60: {1,2,3,4,5,6,...,30,60}
%e 420: {1,2,3,4,5,6,7,...,210,420}
%e 840: {1,2,3,4,5,6,7,8,...,420,840}
%e (End)
%t tav=Table[Length/@Split[Divisors[n],#2==#1+1&],{n,10000}];
%t Table[Position[tav,i][[1,1]],{i,Split[Union@@tav,#2==#1+1&][[1]]}] (* Assumes there are no zeros. - _Gus Wiseman_, Oct 16 2019 *)
%Y The version taking only the longest run is A328449.
%Y The longest run of divisors of n has length A055874(n).
%Y Numbers whose divisors > 1 have no non-singleton runs are A088725.
%Y The number of successive pairs of divisors of n is A129308(n).
%Y Cf. A000005, A003418, A027750, A060775, A181064, A199970, A328166, A328448.
%K nonn
%O 1,2
%A _Matthew Vandermast_, Oct 07 2010
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