A328448 Smallest number whose divisors > 1 have a longest run of length n, and 0 if none exists.

2, 6, 12, 504, 60, 420, 840, 4084080, 2520, 21162960, 27720, 2059318800, 0, 360360, 720720, 8494326640800, 12252240, 281206918792800, 0, 0, 232792560, 409547311252279200, 5354228880, 619808900849199341280, 26771144400, 54749786241679275146400, 80313433200, 5663770990518545704800

Offset

1,1

Links

Table of n, a(n) for n=1..28.

Example

The runs of divisors of 504 (greater than 1) are {{2,3,4},{6,7,8,9},{12},{14},{18},{21},{24},{28},{36},{42},{56},{63},{72},{84},{126},{168},{252},{504}}, the longest of which has length 4, and 504 is the smallest number with this property, so a(4) = 504.

Crossrefs

The version that looks at all divisors (including 1) is A328449.

The longest run of divisors of n greater than 1 has length A328457.

Numbers whose divisors > 1 have no non-singleton runs are A088725.

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).

Cf. A000005, A027750, A055874, A060680, A181063, A199970, A328450.

Sequence in context: A058046 A298410 A367314 * A074180 A126293 A007668

Adjacent sequences: A328445 A328446 A328447 * A328449 A328450 A328451

Keyword

nonn

Author

Gus Wiseman, Oct 16 2019

Extensions

Data corrected and extended by Giovanni Resta, Oct 18 2019

Status

approved