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A339195

Triangle of squarefree numbers grouped by greatest prime factor, read by rows.

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

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OFFSET

1,1

COMMENTS

Also Heinz numbers of subsets of {1..n} that contain n, where the Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

A019565 in its triangle form, but omitting its initial row and with each row's terms in increasing order. - Peter Munn, Feb 26 2021

LINKS

Table of n, a(n) for n=1..63.

FORMULA

For n > 1, T(n,k) = prime(n) * A261144(n-1,k).

EXAMPLE

Triangle begins:

3 6

5 10 15 30

7 14 21 35 42 70 105 210

MATHEMATICA

Table[Prime[n]*Sort[Times@@Prime/@#&/@Subsets[Range[n-1]]], {n, 5}]

CROSSREFS

A000079 (shifted left) gives row lengths.

A339360 gives row sums.

A000040 is column k = 1.

A100484 is column k = 2.

A001748 is column k = 3.

A002110 is column k = 2^(n-1).

A070826 is column k = 2^(n-1) - 1.

A209862 takes prime indices to binary indices in these terms.

A246867 groups squarefree numbers by Heinz weight, with row sums A147655.

A261144 divides the n-th row by prime(n), with row sums A054640.

A339116 is the restriction to semiprimes, with row sums A339194.

A005117 lists squarefree numbers, ordered lexicographically by prime factors: A019565.

A006881 lists squarefree semiprimes.

A072047 counts prime factors of squarefree numbers.

A319246 is the sum of prime indices of the n-th squarefree number.

A329631 lists prime indices of squarefree numbers, reversed: A319247.

A338899/A270650/A270652 give the prime indices of squarefree semiprimes.

Cf. A001221, A014342, A014466, A098350, A112798, A320656, A326882, A338901.

Sequence in context: A073740 A239956 A077320 * A344085 A019565 A309840

Adjacent sequences: A339192 A339193 A339194 * A339196 A339197 A339198

KEYWORD

nonn,tabf

AUTHOR

Gus Wiseman, Dec 02 2020

STATUS

approved