A333483 Sort all positive integers, first by sum of prime indices (A056239), then by number of prime indices (A001222).

1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 12, 16, 11, 14, 15, 18, 20, 24, 32, 13, 21, 22, 25, 27, 28, 30, 36, 40, 48, 64, 17, 26, 33, 35, 42, 44, 45, 50, 54, 56, 60, 72, 80, 96, 128, 19, 34, 39, 49, 55, 52, 63, 66, 70, 75, 81, 84, 88, 90, 100, 108, 112, 120, 144, 160, 192, 256, 23, 38, 51, 65, 77, 68, 78, 98, 99, 105, 110, 125, 104, 126, 132, 135, 140, 150, 162, 168, 176, 180, 200, 216, 224, 240, 288, 320, 384, 512

Offset

0,2

Comments

A refinement of A215366, from which it first differs at a(49) = 55, A215366(49) = 52.

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..96.

OEIS Wiki, Orderings of partitions

Wikiversity, Lexicographic and colexicographic order

Example

Triangle begins:
   1
   2
   3   4
   5   6   8
   7   9  10  12  16
  11  14  15  18  20  24  32
  13  21  22  25  27  28  30  36  40  48  64
  17  26  33  35  42  44  45  50  54  56  60  72  80  96 128

Mathematica

Join@@@Table[Sort[Times@@Prime/@#&/@IntegerPartitions[n, {k}]], {n, 0, 8}, {k, 0, n}]

Crossrefs

Row lengths are A000041.

Ignoring length gives A215366 (graded Heinz numbers).

Sorting by decreasing length gives A333484.

Finally sorting lexicographically by prime indices gives A185974.

Finally sorting colexicographically by prime indices gives A334433.

Finally sorting reverse-lexicographically by prime indices gives A334435.

Finally sorting reverse-colexicographically by prime indices gives A334438.

Number of prime indices is A001222.

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.

Sorting reversed partitions by Heinz number gives A112798.

Sorting partitions by Heinz number gives A296150.

Cf. A026791, A124734, A129129, A193073, A211992, A228100, A333219, A334301, A334434, A334439, A334441, A334442.

Sequence in context: A334111 A243571 A215366 * A334433 A334435 A334436

Adjacent sequences: A333480 A333481 A333482 * A333484 A333485 A333486

Keyword

nonn,tabf

Author

Gus Wiseman, May 10 2020

Status

approved