A328025 Irregular triangle read by rows where row n gives the differences between consecutive divisors of n in weakly decreasing order.

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

Offset

1,2

Links

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

Example

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

Mathematica

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

Crossrefs

Same as A193829 with rows sorted in weakly decreasing order.

Same as A328027 with rows reversed.

Row sums are A001477.

Row lengths are A000005.

First column is A060681.

Heinz numbers of rows are A328023.

Cf. A027750, A060680, A060682, A060683, A070211, A129308, A328024.

Sequence in context: A212320 A197376 A113072 * A305326 A122918 A177424

Adjacent sequences: A328022 A328023 A328024 * A328026 A328027 A328028

Keyword

nonn,tabf

Author

Gus Wiseman, Oct 02 2019

Status

approved