A328450 Numbers that are a smallest number with k pairs of successive divisors, for some k.

1, 2, 6, 12, 60, 72, 180, 360, 420, 840, 1260, 2520, 3780, 5040, 13860, 27720, 36960, 41580, 55440, 83160, 166320, 277200, 360360, 471240, 491400, 720720, 1081080, 1113840, 2162160, 2827440, 3341520, 4324320, 5405400, 6126120

Offset: 0

Author

Gus Wiseman, Oct 15 2019

Keywords

• nonn

Comments

A sorted version of A287142.

Examples

			The divisors of 72 are {1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72}, with pairs of successive divisors {{1, 2}, {2, 3}, {3, 4}, {8, 9}}, and no smaller number has 4 successive pairs, so 72 belongs to the sequence.
		

Crossrefs

Sorted positions of first appearances in A129308.

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

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

The Heinz number of the multiset of run-lengths of divisors of n is A328166(n).

The smallest number whose divisors have a longest run of length n is A328449(n).

Cf. A000005, A003601, A027750, A033676, A060680, A060681, A072627, A181063, A199970, A287142, A328165.

Programs

Mathematica

dat=Table[Count[Differences[Divisors[n]],1],{n,10000}];
Sort[Table[Position[dat,i][[1,1]],{i,Union[dat]}]]