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

0, 1, 2, 6, 12, 0, 60, 420, 840, 0, 2520, 0, 27720, 0, 0, 360360, 720720, 0, 12252240, 0, 0, 0, 232792560, 0, 5354228880, 0, 26771144400, 0, 80313433200, 0, 2329089562800, 72201776446800, 0, 0, 0, 0, 144403552893600, 0, 0, 0, 5342931457063200, 0

Offset: 0

Author

Gus Wiseman, Oct 16 2019

Keywords

• nonn

Links

• Wikipedia, Run (cards)

Crossrefs

Positions of 0's are 0 followed by A024619 - 1.

The version that looks only at all divisors > 1 is A328448.

The longest run of divisors of n has length A055874.

The longest run of divisors of n greater than one has length A328457.

Numbers whose divisors have no non-singleton runs are A005408.

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

The Heinz number of the multiset of run-lengths of divisors of n is A328166(n).

The smallest number whose divisors have a (not necessarily longest) maximal run of length n is A181063.

Cf. A000005, A003601, A027750, A033676, A060680, A060681, A199970, A328195.

Programs

Mathematica

tav=Table[Max@@Length/@Split[Divisors[n],#2==#1+1&],{n,10000}];
Table[If[FreeQ[tav,i],0,Position[tav,i][[1,1]]],{i,0,Max@@tav}]

Formula

a(n) = LCM(1,2,...,n) = A003418(n) if n + 1 is a prime power, otherwise a(n) = 0.