A328165 Numbers whose divisors do not have weakly decreasing run-lengths.

56, 72, 110, 112, 132, 144, 156, 182, 210, 216, 224, 240, 264, 272, 288, 306, 312, 342, 364, 380, 392, 396, 420, 432, 440, 448, 462, 468, 480, 506, 528, 544, 550, 552, 576, 600, 612, 616, 624, 648, 650, 684, 702, 720, 728, 756, 760, 770, 780, 784, 792, 812

Offset: 1

Author

Gus Wiseman, Oct 07 2019

Keywords

• nonn

Examples

			The divisors of 56 are {1, 2, 4, 7, 8, 14, 28, 56}, with runs {{1, 2}, {4}, {7, 8}, {14}, {28}, {56}}, with lengths (2, 1, 2, 1, 1, 1), which are not weakly decreasing, so 56 is in the sequence.
		

Links

• Wikipedia, Run (cards)

Crossrefs

The longest run of divisors of n has length A055874(n).

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, A033676, A060680, A060775, A119313, A181063, A199970.

Programs

Mathematica

Select[Range[1000],!GreaterEqual@@Length/@Split[Divisors[#],#2==#1+1&]&]