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

1,1

Links

Table of n, a(n) for n=1..52.

Wikipedia, Run (cards)

Example

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.

Mathematica

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

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.

Sequence in context: A043158 A039335 A043938 * A214250 A286981 A254369

Adjacent sequences: A328162 A328163 A328164 * A328166 A328167 A328168

Keyword

nonn

Author

Gus Wiseman, Oct 07 2019

Status

approved