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A358106
Quotient of the n-th divisible pair, where pairs are ordered first by sum and then by denominator.
6
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
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.
Sequence in context: A376930 A229137 A358631 * A282510 A131225 A221919
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Nov 03 2022
STATUS
approved