A358106 - OEIS

%I #7 Nov 04 2022 14:44:25

%S 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,

%T 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,

%U 24,4,25,12,1,26,8,2,27,13,6,3,1,28,29,14,9,5,4,2,1

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

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

%e Grouping by sum gives:

%e    2:  1

%e    3:  2

%e    4:  3 1

%e    5:  4

%e    6:  5 2 1

%e    7:  6

%e    8:  7 3 1

%e    9:  8 2

%e   10:  9 4 1

%e   11: 10

%e   12: 11 5 3 2 1

%e   13: 12

%e   14: 13 6 1

%e   15: 14 4 2

%e   16: 15 7 3 1

%e   17: 16

%e   18: 17 8 5 2 1

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

%Y Row-lengths are A032741.

%Y This is A208460/A027751.

%Y A ranking of divisible pairs is A318990, proper A339005.

%Y A different ordering is A358103 = A358104 / A358105.

%Y A000041 counts partitions, strict A000009.

%Y A001358 lists semiprimes, squarefree A006881.

%Y A318991 ranks divisor-chains.

%Y A358192/A358193 gives quotients of semiprime indices.

%Y Cf. A000837, A003238, A122934.

%K nonn,tabf

%O 2,2

%A _Gus Wiseman_, Nov 03 2022