A265110 Partial row products of table A027746, prime factors with repetition.

1, 2, 3, 2, 4, 5, 2, 6, 7, 2, 4, 8, 3, 9, 2, 10, 11, 2, 4, 12, 13, 2, 14, 3, 15, 2, 4, 8, 16, 17, 2, 6, 18, 19, 2, 4, 20, 3, 21, 2, 22, 23, 2, 4, 8, 24, 5, 25, 2, 26, 3, 9, 27, 2, 4, 28, 29, 2, 6, 30, 31, 2, 4, 8, 16, 32, 3, 33, 2, 34, 5, 35, 2, 4, 12, 36

Offset: 1

Author

Reinhard Zumkeller, Dec 01 2015

Keywords

• nonn
• tabf

Comments

T(n,1) = A020639(n); T(n,A001222(n)) = n.

Examples

			.   n |   T(n,*)       |   A027746(n,*)
. ----+----------------+----------------
.   1 |   1            |   1
.   2 |   2            |   2
.   3 |   3            |   3
.   4 |   2, 4         |   2, 2
.   5 |   5            |   5
.   6 |   2, 6         |   2, 3
.   7 |   7            |   7
.   8 |   2, 4, 8      |   2, 2, 2
.   9 |   3, 9         |   3, 3
.  10 |   2, 10        |   2, 5
.  11 |   11           |   11
.  12 |   2, 4, 12     |   2, 2, 3
.  13 |   13           |   13
.  14 |   2, 14        |   2, 7
.  15 |   3, 15        |   3, 5
.  16 |   2, 4, 8, 16  |   2, 2, 2, 2
.  17 |   17           |   17
.  18 |   2, 6, 18     |   2, 3, 3
.  19 |   19           |   19
.  20 |   2, 4, 20     |   2, 2, 5
		

Links

• Reinhard Zumkeller, Rows n = 1..1000 of triangle, flattened

Crossrefs

Cf. A027746, A175943, A001222 (row lengths), A020639.

Programs

Haskell

a265110 n k = a265110_tabf !! (n-1) !! (k-1)
a265110_row n = a265110_tabf !! (n-1)
a265110_tabf = map (scanl1 (*)) a027746_tabf

Mathematica

Table[FoldList[Times, Flatten[FactorInteger[n] /. {p_, e_} /; e > 0 :> ConstantArray[p, e]]], {n, 37}] // Flatten (* Michael De Vlieger, Apr 28 2017 *)

Formula

T(n,k) = product(A027747(n,k): k = 1 .. A001221(n)).