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.

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

Offset: 1

Author

Reinhard Zumkeller, Jul 25 2014

Keywords

• nonn
• tabf

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)

Examples

			.    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 .
		

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

Crossrefs

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

Programs

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 *)

Extensions

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