cp's OEIS Frontend

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

%I A358106 #7 Nov 04 2022 14:44:25
%S A358106 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 A358106 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 A358106 24,4,25,12,1,26,8,2,27,13,6,3,1,28,29,14,9,5,4,2,1
%N A358106 Quotient of the n-th divisible pair, where pairs are ordered first by sum and then by denominator.
%F A358106 a(n) = A208460(n)/A027751(n).
%e A358106 Grouping by sum gives:
%e A358106    2:  1
%e A358106    3:  2
%e A358106    4:  3 1
%e A358106    5:  4
%e A358106    6:  5 2 1
%e A358106    7:  6
%e A358106    8:  7 3 1
%e A358106    9:  8 2
%e A358106   10:  9 4 1
%e A358106   11: 10
%e A358106   12: 11 5 3 2 1
%e A358106   13: 12
%e A358106   14: 13 6 1
%e A358106   15: 14 4 2
%e A358106   16: 15 7 3 1
%e A358106   17: 16
%e A358106   18: 17 8 5 2 1
%t A358106 Table[Divide@@@Select[IntegerPartitions[n,{2}],Divisible@@#&],{n,2,30}]
%Y A358106 Row-lengths are A032741.
%Y A358106 This is A208460/A027751.
%Y A358106 A ranking of divisible pairs is A318990, proper A339005.
%Y A358106 A different ordering is A358103 = A358104 / A358105.
%Y A358106 A000041 counts partitions, strict A000009.
%Y A358106 A001358 lists semiprimes, squarefree A006881.
%Y A358106 A318991 ranks divisor-chains.
%Y A358106 A358192/A358193 gives quotients of semiprime indices.
%Y A358106 Cf. A000837, A003238, A122934.
%K A358106 nonn,tabf
%O A358106 2,2
%A A358106 _Gus Wiseman_, Nov 03 2022