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

1,2

Comments

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

Links

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

Formula

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

Example

.   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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A214595 A357255 A136181 * A304742 A003976 A252371

Adjacent sequences: A265107 A265108 A265109 * A265111 A265112 A265113

Keyword

nonn,tabf

Author

Reinhard Zumkeller, Dec 01 2015

Status

approved