login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A339195 Triangle of squarefree numbers grouped by greatest prime factor, read by rows. 4
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 (list; graph; refs; listen; history; text; internal format)
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:

   2

   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 * A019565 A309840 A340316

Adjacent sequences:  A339192 A339193 A339194 * A339196 A339197 A339198

KEYWORD

nonn,tabf

AUTHOR

Gus Wiseman, Dec 02 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 6 14:16 EDT 2021. Contains 343586 sequences. (Running on oeis4.)