A251715 Array: A251637(n,k) / prime(n).

1, 1, 2, 3, 3, 4, 2, 1, 5, 7, 2, 5, 5, 2, 3, 3, 1, 1, 7, 4, 6, 3, 1, 3, 3, 2, 7, 8, 2, 1, 2, 5, 4, 4, 9, 5, 3, 1, 5, 5, 4, 13, 9, 13, 10, 3, 1, 5, 2, 7, 9, 7, 17, 11, 11, 2, 1, 5, 3, 4, 4, 7, 9, 11, 15, 13, 2, 1, 2, 2, 7, 7, 9, 6, 6, 13, 17, 14, 3, 1, 3, 5

Offset

1,3

Comments

T(n,k) = A251637(n,k) / A000040(n);

A251637(n,k) = T(n,k) * A000040(n);

for n > 2: T(n,1) = A251619(n);

conjecture: A098550 is a permutation of the positive integers iff all rows are permutations of the positive integers.

For third column with row numbers > 4: see A251542. - Reinhard Zumkeller, Dec 16 2014

Links

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Example

.   n   p |  A251637(n,k) / p, with p = prime(n), n = 1..25, k = 1..20
.  -------+-----------------------------------------------------------
.   1   2 |  1 2 4 7 3  6 8  5 10 11 13 14 16  9 12 17 18 15 19 21 22
.   2   3 |  1 3 5 2 4  7 9 13 11 15 17  6  8 12 10 21 14 19 23 16 25
.   3   5 |  3 1 5 7 2  4 9 17 11 13  6 19  8 10 23 15 12 35 21 14 16
.   4   7 |  2 5 1 3 4 13 7  9  6  8 11 17 19 23 25 15 10 12 47 29 21
.   5  11 |  2 1 3 5 4  9 7  6  8 15 13 11 17 10 12 21 19 14 16 25 18
.   6  13 |  3 1 2 5 7  4 9  6  8 15 11 10 12 17 13 19 21 14 16 23 25
.   7  17 |  3 1 5 2 4  7 9  6 11  8 10 15 13 12 14 21 17 16 19 23 25
.   8  19 |  2 1 5 3 7  4 9  6  8 11 13 10 15 12 14 21 17 19 23 16 25
.   9  23 |  3 1 5 2 7  4 6  9  8 11 13 15 10 12 19 17 14 21 16 25 18
.  10  29 |  3 1 2 5 7  4 6  9  8 11 13 10 15 12 17 14 21 19 16 25 23
.  11  31 |  2 1 3 5 4  7 9  6 11 13  8 15 10 12 17 19 14 21 16 23 18
.  12  37 |  2 1 3 5 4  7 6  9  8 11 15 10 17 13 12 23 19 21 14 16 18
.  13  41 |  3 1 2 5 4  7 6  9 11  8 10 13 15 12 17 14 21 19 16 25 23
.  14  43 |  2 1 3 5 4  7 9  6 11  8 10 15 13 12 14 19 17 21 16 23 18
.  15  47 |  2 1 7 3 5  4 6  9 11  8 10 13 15 12 17 19 14 21 16 23 25
.  16  53 |  2 1 5 3 4  7 6  9  8 11 13 10 15 12 17 14 21 19 16 18 25
.  17  59 |  2 1 3 5 4  7 6  9 11  8 13 10 15 17 12 14 19 21 16 23 18
.  18  61 |  2 1 7 3 5  4 6  9 11  8 13 10 15 12 17 14 19 21 16 23 18
.  19  67 |  3 1 5 2 4  7 9  6  8 11 13 10 15 12 17 14 19 21 16 23 18
.  20  71 |  2 1 3 5 4  7 6  9  8 11 10 15 13 12 17 14 19 21 16 23 18
.  21  73 |  2 1 5 3 4  7 6  9  8 11 10 13 15 12 17 14 19 21 16 23 18
.  22  79 |  2 1 3 5 4  7 6  9  8 11 13 10 15 12 14 17 19 21 16 23 18
.  23  83 |  3 1 7 2 5  4 6  9 11  8 13 10 15 12 17 19 14 21 16 23 18
.  24  89 |  2 1 3 5 4  7 6  9  8 11 13 10 15 12 17 14 21 19 16 23 18
.  25  97 |  3 1 7 2 5  4 6  9 11  8 10 13 15 12 17 14 19 21 16 23 18 .
.  --------------------------------------------------------------------
See table A251637 for T(n,k) * p.

Crossrefs

Cf. A098550, A251637, A000040, A251619.

Sequence in context: A337307 A357372 A316910 * A361819 A304758 A103893

Adjacent sequences: A251712 A251713 A251714 * A251716 A251717 A251718

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Dec 09 2014

Extensions

Wrong data replaced; Reinhard Zumkeller, Dec 15 2014

Status

approved