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

Author

Gus Wiseman, Nov 03 2022

Keywords

• nonn
• tabf

Examples

			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
		

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.

Programs

Mathematica

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

Formula

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