A328027 Irregular triangle read by rows where row n lists, in weakly increasing order, the differences between consecutive divisors of n.

1, 2, 1, 2, 4, 1, 1, 3, 6, 1, 2, 4, 2, 6, 1, 3, 5, 10, 1, 1, 1, 2, 6, 12, 1, 5, 7, 2, 2, 10, 1, 2, 4, 8, 16, 1, 1, 3, 3, 9, 18, 1, 1, 2, 5, 10, 2, 4, 14, 1, 9, 11, 22, 1, 1, 1, 2, 2, 4, 12, 4, 20, 1, 11, 13, 2, 6, 18, 1, 2, 3, 7, 14, 28, 1, 1, 1, 2, 4, 5, 15

Offset

1,2

Links

Table of n, a(n) for n=1..81.

Example

Triangle begins:
   {}
   1
   2
   1  2
   4
   1  1  3
   6
   1  2  4
   2  6
   1  3  5
  10
   1  1  1  2  6
  12
   1  5  7
   2  2 10
   1  2  4  8
  16
   1  1  3  3  9
  18
   1  1  2  5 10
   2  4 14
   1  9 11
  22
   1  1  1  2  2  4 12
For example, the divisors of 18 are {1,2,3,6,9,18}, with differences {1,1,3,3,9}, which is row 18.

Mathematica

Table[Sort[Differences[Divisors[n]]], {n, 30}]

Crossrefs

Same as A193829 with rows sorted in increasing order.

Same as A328025 with rows reversed.

Row sums are A001477.

Row lengths are A000005.

First column is A060680.

Cf. A027750, A060681, A060682, A060683, A070211, A129308, A328024.

Sequence in context: A097865 A105245 A105246 * A193829 A337714 A198069

Adjacent sequences: A328024 A328025 A328026 * A328028 A328029 A328030

Keyword

nonn,tabf

Author

Gus Wiseman, Oct 02 2019

Status

approved