A348475 a(n) = Product_{k=1..A003056(n)} prime(T(n,k)), where T(n,k) = k-th term in row n of A235791.

2, 3, 10, 14, 33, 78, 170, 190, 483, 1218, 2046, 4070, 5330, 8385, 33558, 37842, 47082, 127490, 169510, 269445, 825630, 1250886, 1404858, 1969926, 4270910, 6988190, 13239105, 27506490, 29387490, 61019322, 74958702, 77319606, 191617790, 254235170, 715103895, 1549364190

Offset

1,1

Comments

Prime product compactification of A235791.

All terms are squarefree.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

Row 3 of A235791 contains {3,1}, thus, a(3) = prime(3)*prime(1) = 5*2 = 10.
Omar E. Pol's diagram of rows of A235791:
.                                    y    row a(n) of A067255*   a(n)
Row                                 _|    --------------------------
1                                 _|1| -> 1                 =      2
2                               _|2 _| -> .1                =      3
3                             _|3  |1| -> 1.1               =     10
4                           _|4   _|1| -> 1..1              =     14
5                         _|5    |2 _| -> .1..1             =     33
6                       _|6     _|2|1| -> 11...1            =     78
7                     _|7      |3  |1| -> 1.1...1           =    170
8                   _|8       _|3 _|1| -> 1.1....1          =    190
9                 _|9        |4  |2 _| -> .1.1....1         =    483
10              _|10        _|4  |2|1| -> 11.1.....1        =   1218
11            _|11         |5   _|2|1| -> 11..1.....1       =   2046
12          _|12          _|5  |3  |1| -> 1.1.1......1      =   4070
13        _|13           |6    |3 _|1| -> 1.1..1......1     =   5330
14      _|14            _|6   _|3|2 _| -> .11..1.......1    =   8385
15    _|15             |7    |4  |2|1| -> 11.1..1.......1   =  33558
16  _|16              _|7    |4  |2|1| -> 11.1..1........1  =  37842
...
* we replace 0 with "." for clarity.

Mathematica

Table[Times @@ Array[Prime@ Ceiling[(n + 1)/# - (# + 1)/2] &, Floor[(Sqrt[8 n + 1] - 1)/2]], {n, 35}]
(* Use the b-file to generate k rows of A235791 *)
With[{k = 120}, MapIndexed[Reverse[PrimePi /@ FactorInteger[#][[All, 1]]] &, Import["https://oeis.org/A348475/b348475.txt", "Data"][[1 ;; k, -1]]]] (* Michael De Vlieger, Oct 21 2021 *)

Crossrefs

Cf. A000040, A003056, A067255, A235791.

Sequence in context: A299205 A268878 A194544 * A075770 A135101 A108065

Adjacent sequences: A348472 A348473 A348474 * A348476 A348477 A348478

Keyword

nonn,easy

Author

Michael De Vlieger, Oct 19 2021

Status

approved