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A278104 Irregular triangle T(n,k) := A277648(n,k) for k = 1...A278102(n), read by rows. 4
1, 2, 1, 3, 2, 1, 4, 2, 5, 3, 2, 6, 4, 3, 2, 7, 4, 8, 5, 4, 3, 9, 6, 10, 7, 5, 11, 7, 12, 8, 6, 13, 9, 7, 5, 14, 9, 15, 10, 8, 6, 16, 11, 17, 12, 9, 18, 12, 19, 13, 10, 20, 14, 11, 8, 21, 14, 22, 15, 12, 9, 8, 23, 16, 13, 10, 9, 8, 24, 16, 13, 10, 9, 25, 17, 26, 18, 27, 19, 15, 28, 19 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This triangle lists the "descending sequences across ranks" of Eggleton et al.

REFERENCES

R. B. Eggleton, J. S. Kimberley and J. A. MacDougall, Square-free rank of integers, submitted.

LINKS

Jason Kimberley, Table of n, a(n) for n = 1..10001 (the first 3304 rows of the triangle)

EXAMPLE

The first 23 rows are:

1;

2,  1;

3,  2,  1;

4,  2;

5,  3,  2;

6,  4,  3,  2;

7,  4;

8,  5,  4,  3;

9,  6;

10,  7,  5;

11,  7;

12,  8,  6;

13,  9,  7,  5;

14,  9;

15, 10,  8,  6;

16, 11;

17, 12,  9;

18, 12;

19, 13, 10;

20, 14, 11,  8;

21, 14;

22, 15, 12,  9,  8;

23, 16, 13, 10,  9,  8;

MATHEMATICA

Map[Last, #, {2}] &@ Map[TakeWhile[FoldList[Function[s, Boole[s < 0] {First@ #2, Last@ #2}][First@ #2 - First@ #1] &, #], Total@ # > 0 &] &, #] &@ Map[DeleteCases[#, {0, 0}] &, Table[Boole[SquareFreeQ@ k] {k #^2, #} &@ Floor[n/Sqrt@ k], {n, 32}, {k, n^2}] ] // Flatten (* Michael De Vlieger, Nov 24 2016 *)

PROG

(Magma)

A277647:=func<n, k|Isqrt(n^2 div k)>;

A277648_row:=func<n|[A277647(n, k):k in[1..n^2]|IsSquarefree(k)]>;

A278101_row:=func<n|[A277647(n, k)^2*k:k in[1..n^2]|IsSquarefree(k)]>;

A278104_row:=func<n|(exists(dec){A277648_row(n)[1..j]:j in[1..#row-1]|row[j]le row[j+1]}select dec else[1]) where row is A278101_row(n) >;

&cat[A278104_row(n):n in[1..23]];

CROSSREFS

Sequence in context: A337632 A057058 A334441 * A141672 A141671 A309596

Adjacent sequences:  A278101 A278102 A278103 * A278105 A278106 A278107

KEYWORD

nonn,tabf,easy

AUTHOR

Jason Kimberley, Nov 15 2016

STATUS

approved

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Last modified June 24 17:31 EDT 2021. Contains 345417 sequences. (Running on oeis4.)