A333484 Sort all positive integers, first by sum of prime indices (A056239), then by decreasing number of prime indices (A001222).

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.

Links

Table of n, a(n) for n=0..66.

OEIS Wiki, Orderings of partitions

Wikiversity, Lexicographic and colexicographic order

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.

Cf. A124734, A129129, A211992, A228100, A333219, A334301, A334433, A334434, A334439, A334441, A334442.

Sequence in context: A245613 A260431 A376738 * A334434 A333485 A246166

Adjacent sequences: A333481 A333482 A333483 * A333485 A333486 A333487

Keyword

nonn,tabf

Author

Gus Wiseman, May 10 2020

Status

approved