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A245499 Table read by rows: n-th row contains the factors which occur when constructing R. L. Graham's sequence A006255, such that the number of factors and also the product is minimal. 9
1, 2, 3, 6, 3, 6, 8, 4, 5, 8, 10, 6, 8, 12, 7, 8, 14, 8, 10, 12, 15, 9, 10, 12, 15, 18, 11, 18, 22, 12, 15, 20, 13, 18, 26, 14, 15, 18, 20, 21, 15, 18, 20, 24, 16, 17, 18, 34, 18, 24, 27, 19, 32, 38, 20, 24, 30, 21, 27, 28, 22, 24, 33, 23, 32, 46, 24, 27, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A066400(n) = length of n-th row.

A006255(n) = T(n,A066400(n)), last term in n-th row.

A245530(n) = A066401(n)^2 = product of n-th row.

For n > 2: A245508(n) = T(A000040(n),2).

T(n,k) denote b_k in the definition given in A006255.

From David A. Corneth, Oct 22 2016 and Oct 25 2016: (Start)

Frequency of n in this sequence: 1, 1, 2, 1, 1, 3, 1, 5, 1, 3, 1, 4, 1, 2, ... See A277606.

Primes and squares occur once in this sequence except for 3 which occurs twice.

In the first 10000 rows, 9522 occurs most often and appears 60 times. 6498 is a close second with 59 occurrences.

(End)

REFERENCES

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 2nd. ed., Problem 4.39, pages 147, 616, 533.

LINKS

Peter Kagey, Table of n, a(n) for n = 1..44055 (Derived from David A. Corneth's unflattened file)

David A. Corneth, First 10000 rows unflattened

EXAMPLE

.    n |  Row(n)                | A066400(n) | A245530(n) | A066401(n)

. -----+------------------------+------------+------------+-----------

.    1 |  [1]                   |          1 |          1 |          1

.    2 |  [2, 3, 6]             |          3 |         36 |          6

.    3 |  [3, 6, 8]             |          3 |        144 |         12

.    4 |  [4]                   |          1 |          4 |          2

.    5 |  [5, 8, 10]            |          3 |        400 |         20

.    6 |  [6, 8, 12]            |          3 |        576 |         24

.    7 |  [7, 8, 14]            |          3 |        784 |         28

.    8 |  [8, 10, 12, 15]       |          4 |      14400 |        120

.    9 |  [9]                   |          1 |          9 |          3

.   10 |  [10, 12, 15, 18]      |          4 |      32400 |        180

.   11 |  [11, 18, 22]          |          3 |       4356 |         66

.   12 |  [12, 15, 20]          |          3 |       3600 |         60

.   13 |  [13, 18, 26]          |          3 |       6084 |         78

.   14 |  [14, 15, 18, 20, 21]  |          5 |    1587600 |       1260

.   15 |  [15, 18, 20, 24]      |          4 |     129600 |        360

.   16 |  [16]                  |          1 |         16 |          4

.   17 |  [17, 18, 34]          |          3 |      10404 |        102

.   18 |  [18, 24, 27]          |          3 |      11664 |        108

.   19 |  [19, 32, 38]          |          3 |      23104 |        152

.   20 |  [20, 24, 30]          |          3 |      14400 |        120

.   21 |  [21, 27, 28]          |          3 |      15876 |        126

.   22 |  [22, 24, 33]          |          3 |      17424 |        132

.   23 |  [23, 32, 46]          |          3 |      33856 |        184

.   24 |  [24, 27, 32]          |          3 |      20736 |        144

.   25 |  [25]                  |          1 |         25 |          5 .

MATHEMATICA

Table[k = 0; While[Length@ # == 0 &@ Set[f, Select[Rest@ Subsets@ Range@ k, IntegerQ@ Sqrt[n (Times @@ # &[n + #])] &]], k++]; If[IntegerQ@ Sqrt@ n, k = {n}, k = n + Prepend[First@ f, 0]]; k, {n, 22}] (* Michael De Vlieger, Oct 26 2016 *)

CROSSREFS

Cf. A006255, A006530, A007913, A010051, A010052, A020639, A049084, A066400 (row lengths), A066401, A089229, A151800, A245508, A245530 (row products), A277606.

Sequence in context: A084228 A328571 A275733 * A323642 A193898 A129915

Adjacent sequences:  A245496 A245497 A245498 * A245500 A245501 A245502

KEYWORD

nonn,tabf

AUTHOR

Reinhard Zumkeller, Jul 25 2014

EXTENSIONS

Following a suggestion of Peter Kagey, definition clarified by Reinhard Zumkeller, Nov 28 2014. Also removed erroneous program and b-file.

STATUS

approved

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Last modified January 20 08:18 EST 2020. Contains 331081 sequences. (Running on oeis4.)