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A328449
Smallest number in whose divisors the longest run is of length n, and 0 if none exists.
6
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
0,3
FORMULA
a(n) = LCM(1,2,...,n) = A003418(n) if n + 1 is a prime power, otherwise a(n) = 0.
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}]
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.
Sequence in context: A057294 A342544 A342540 * A293589 A293117 A293122
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 16 2019
STATUS
approved