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A265110 Partial row products of table A027746, prime factors with repetition. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A029638 A136181 * A003976 A252371 A275817

Adjacent sequences:  A265107 A265108 A265109 * A265111 A265112 A265113

KEYWORD

nonn,tabf

AUTHOR

Reinhard Zumkeller, Dec 01 2015

STATUS

approved

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Last modified December 11 13:46 EST 2017. Contains 295876 sequences.