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A328449 Smallest number in whose divisors the longest run is of length n, and 0 if none exists.

%I A328449 #7 Oct 18 2019 16:45:09
%S A328449 0,1,2,6,12,0,60,420,840,0,2520,0,27720,0,0,360360,720720,0,12252240,
%T A328449 0,0,0,232792560,0,5354228880,0,26771144400,0,80313433200,0,
%U A328449 2329089562800,72201776446800,0,0,0,0,144403552893600,0,0,0,5342931457063200,0
%N A328449 Smallest number in whose divisors the longest run is of length n, and 0 if none exists.
%H A328449 Wikipedia, <a href="https://en.wikipedia.org/wiki/Run_(cards)">Run (cards)</a>
%F A328449 a(n) = LCM(1,2,...,n) = A003418(n) if n + 1 is a prime power, otherwise a(n) = 0.
%t A328449 tav=Table[Max@@Length/@Split[Divisors[n],#2==#1+1&],{n,10000}];
%t A328449 Table[If[FreeQ[tav,i],0,Position[tav,i][[1,1]]],{i,0,Max@@tav}]
%Y A328449 Positions of 0's are 0 followed by A024619 - 1.
%Y A328449 The version that looks only at all divisors > 1 is A328448.
%Y A328449 The longest run of divisors of n has length A055874.
%Y A328449 The longest run of divisors of n greater than one has length A328457.
%Y A328449 Numbers whose divisors have no non-singleton runs are A005408.
%Y A328449 The number of successive pairs of divisors of n is A129308(n).
%Y A328449 The Heinz number of the multiset of run-lengths of divisors of n is A328166(n).
%Y A328449 The smallest number whose divisors have a (not necessarily longest) maximal run of length n is A181063.
%Y A328449 Cf. A000005, A003601, A027750, A033676, A060680, A060681, A199970, A328195.
%K A328449 nonn
%O A328449 0,3
%A A328449 _Gus Wiseman_, Oct 16 2019