A344085 - OEIS

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A344085

Triangle of squarefree numbers first grouped by greatest prime factor, then sorted by Omega, then in increasing order, read by rows.

1, 2, 3, 6, 5, 10, 15, 30, 7, 14, 21, 35, 42, 70, 105, 210, 11, 22, 33, 55, 77, 66, 110, 154, 165, 231, 385, 330, 462, 770, 1155, 2310, 13, 26, 39, 65, 91, 143, 78, 130, 182, 195, 273, 286, 429, 455, 715, 1001, 390, 546, 858, 910, 1365, 1430, 2002, 2145, 3003, 5005, 2730, 4290, 6006, 10010, 15015, 30030

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OFFSET

1,2

COMMENTS

Differs from A339195 in having 77 before 66.

LINKS

Table of n, a(n) for n=1..64.

EXAMPLE

Triangle begins:

3 6

5 10 15 30

7 14 21 35 42 70 105 210

MATHEMATICA

nn=4;

GatherBy[SortBy[Select[Range[Times@@Prime/@Range[nn]], SquareFreeQ[#]&&PrimePi[FactorInteger[#][[-1, 1]]]<=nn&], PrimeOmega], FactorInteger[#][[-1, 1]]&]

CROSSREFS

Row lengths are A000079.

Grouping by greatest prime factor only gives A339195.

Row sums are 1 and A339360.

Cf. A005117, A005183, A014466, A209862.

Partition/composition orderings: A026791, A026792, A026793, A036036, A036037, A048793, A066099, A080577, A112798, A118457, A124734, A162247, A193073, A211992, A228100, A228531, A246688, A272020, A299755, A296774, A304038, A319247, A329631, A334301, A334302, A334439, A334442, A335122, A344086, A344087, A344088, A344089.

Partition/composition applications: A001793, A036043, A049085, A070939, A115623, A124736, A129129, A185974, A238966, A294648, A333483, A333484, A333485, A333486, A334433, A334434, A334435, A334436, A334437, A334438, A334440, A334441, A335123, A335124.

Sequence in context: A239956 A077320 A339195 * A019565 A309840 A377566

Adjacent sequences: A344082 A344083 A344084 * A344086 A344087 A344088

KEYWORD

nonn,tabf

AUTHOR

Gus Wiseman, May 11 2021

STATUS

approved