A358106 Quotient of the n-th divisible pair, where pairs are ordered first by sum and then by denominator.

1, 2, 3, 1, 4, 5, 2, 1, 6, 7, 3, 1, 8, 2, 9, 4, 1, 10, 11, 5, 3, 2, 1, 12, 13, 6, 1, 14, 4, 2, 15, 7, 3, 1, 16, 17, 8, 5, 2, 1, 18, 19, 9, 4, 3, 1, 20, 6, 2, 21, 10, 1, 22, 23, 11, 7, 5, 3, 2, 1, 24, 4, 25, 12, 1, 26, 8, 2, 27, 13, 6, 3, 1, 28, 29, 14, 9, 5, 4, 2, 1

Offset

2,2

Links

Table of n, a(n) for n=2..82.

Formula

a(n) = A208460(n)/A027751(n).

Example

Grouping by sum gives:
   2:  1
   3:  2
   4:  3 1
   5:  4
   6:  5 2 1
   7:  6
   8:  7 3 1
   9:  8 2
  10:  9 4 1
  11: 10
  12: 11 5 3 2 1
  13: 12
  14: 13 6 1
  15: 14 4 2
  16: 15 7 3 1
  17: 16
  18: 17 8 5 2 1

Mathematica

Table[Divide@@@Select[IntegerPartitions[n, {2}], Divisible@@#&], {n, 2, 30}]

Crossrefs

Row-lengths are A032741.

This is A208460/A027751.

A ranking of divisible pairs is A318990, proper A339005.

A different ordering is A358103 = A358104 / A358105.

A000041 counts partitions, strict A000009.

A001358 lists semiprimes, squarefree A006881.

A318991 ranks divisor-chains.

A358192/A358193 gives quotients of semiprime indices.

Cf. A000837, A003238, A122934.

Sequence in context: A092942 A229137 A358631 * A282510 A131225 A221919

Adjacent sequences: A358103 A358104 A358105 * A358107 A358108 A358109

Keyword

nonn,tabf

Author

Gus Wiseman, Nov 03 2022

Status

approved