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

Author

Gus Wiseman, Oct 16 2019

Keywords

• nonn

Examples

			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.

Extensions

Data corrected and extended by Giovanni Resta, Oct 18 2019