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%I A348475 #9 Oct 22 2021 11:36:17
%S A348475 2,3,10,14,33,78,170,190,483,1218,2046,4070,5330,8385,33558,37842,
%T A348475 47082,127490,169510,269445,825630,1250886,1404858,1969926,4270910,
%U A348475 6988190,13239105,27506490,29387490,61019322,74958702,77319606,191617790,254235170,715103895,1549364190
%N A348475 a(n) = Product_{k=1..A003056(n)} prime(T(n,k)), where T(n,k) = k-th term in row n of A235791.
%C A348475 Prime product compactification of A235791.
%C A348475 All terms are squarefree.
%H A348475 Michael De Vlieger, <a href="/A348475/b348475.txt">Table of n, a(n) for n = 1..10000</a>
%e A348475 Row 3 of A235791 contains {3,1}, thus, a(3) = prime(3)*prime(1) = 5*2 = 10.
%e A348475 Omar E. Pol's diagram of rows of A235791:
%e A348475 .                                    y    row a(n) of A067255*   a(n)
%e A348475 Row                                 _|    --------------------------
%e A348475 1                                 _|1| -> 1                 =      2
%e A348475 2                               _|2 _| -> .1                =      3
%e A348475 3                             _|3  |1| -> 1.1               =     10
%e A348475 4                           _|4   _|1| -> 1..1              =     14
%e A348475 5                         _|5    |2 _| -> .1..1             =     33
%e A348475 6                       _|6     _|2|1| -> 11...1            =     78
%e A348475 7                     _|7      |3  |1| -> 1.1...1           =    170
%e A348475 8                   _|8       _|3 _|1| -> 1.1....1          =    190
%e A348475 9                 _|9        |4  |2 _| -> .1.1....1         =    483
%e A348475 10              _|10        _|4  |2|1| -> 11.1.....1        =   1218
%e A348475 11            _|11         |5   _|2|1| -> 11..1.....1       =   2046
%e A348475 12          _|12          _|5  |3  |1| -> 1.1.1......1      =   4070
%e A348475 13        _|13           |6    |3 _|1| -> 1.1..1......1     =   5330
%e A348475 14      _|14            _|6   _|3|2 _| -> .11..1.......1    =   8385
%e A348475 15    _|15             |7    |4  |2|1| -> 11.1..1.......1   =  33558
%e A348475 16  _|16              _|7    |4  |2|1| -> 11.1..1........1  =  37842
%e A348475 ...
%e A348475 * we replace 0 with "." for clarity.
%t A348475 Table[Times @@ Array[Prime@ Ceiling[(n + 1)/# - (# + 1)/2] &, Floor[(Sqrt[8 n + 1] - 1)/2]], {n, 35}]
%t A348475 (* Use the b-file to generate k rows of A235791 *)
%t A348475 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 *)
%Y A348475 Cf. A000040, A003056, A067255, A235791.
%K A348475 nonn,easy
%O A348475 1,1
%A A348475 _Michael De Vlieger_, Oct 19 2021

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