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A333484
Sort all positive integers, first by sum of prime indices (A056239), then by decreasing number of prime indices (A001222).
9
1, 2, 4, 3, 8, 6, 5, 16, 12, 9, 10, 7, 32, 24, 18, 20, 14, 15, 11, 64, 48, 36, 40, 27, 28, 30, 21, 22, 25, 13, 128, 96, 72, 80, 54, 56, 60, 42, 44, 45, 50, 26, 33, 35, 17, 256, 192, 144, 160, 108, 112, 120, 81, 84, 88, 90, 100, 52, 63, 66, 70, 75, 34, 39, 49, 55, 19
OFFSET
0,2
COMMENTS
A refinement of A215366.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
EXAMPLE
Triangle begins:
1
2
4 3
8 6 5
16 12 9 10 7
32 24 18 20 14 15 11
64 48 36 40 27 28 30 21 22 25 13
128 96 72 80 54 56 60 42 44 45 50 26 33 35 17
MATHEMATICA
Join@@@Table[Sort[Times@@Prime/@#&/@IntegerPartitions[n, {k}]], {n, 0, 8}, {k, n, 0, -1}]
CROSSREFS
Row lengths are A000041.
Ignoring length gives A215366 (graded Heinz numbers).
Sorting by increasing length gives A333483.
Number of prime indices is A001222.
Lexicographically ordered reversed partitions are A026791.
Reversed partitions in Abramowitz-Stegun (sum/length/lex) order are A036036.
Partitions in (sum/length/colex) order are A036037.
Sum of prime indices is A056239.
Reverse-lexicographically ordered partitions are A080577.
Sorting reversed partitions by Heinz number gives A112798.
Lexicographically ordered partitions are A193073.
Sorting partitions by Heinz number gives A296150.
Sequence in context: A245613 A260431 A376738 * A334434 A333485 A246166
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, May 10 2020
STATUS
approved