cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A325239 Irregular triangle read by rows where row 1 is {1} and row n > 1 is the sequence starting with n and repeatedly applying A181819 until 2 is reached.

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%I A325239 #8 Apr 29 2022 15:54:39
%S A325239 1,2,3,2,4,3,2,5,2,6,4,3,2,7,2,8,5,2,9,3,2,10,4,3,2,11,2,12,6,4,3,2,
%T A325239 13,2,14,4,3,2,15,4,3,2,16,7,2,17,2,18,6,4,3,2,19,2,20,6,4,3,2,21,4,3,
%U A325239 2,22,4,3,2,23,2,24,10,4,3,2,25,3,2,26,4,3,2
%N A325239 Irregular triangle read by rows where row 1 is {1} and row n > 1 is the sequence starting with n and repeatedly applying A181819 until 2 is reached.
%C A325239 The function A181819 maps n = p^i*...*q^j to prime(i)*...*prime(j) = product of primes indexed by the prime exponents of n.
%H A325239 Michael De Vlieger, <a href="/A325239/b325239.txt">Table of n, a(n) for n = 1..10581</a> (rows 1..2500, flattened)
%H A325239 Michael De Vlieger, <a href="/A325239/a325239.png">For m in row n, plot black else plot white</a>, n = 1..120, 4X magnification.
%H A325239 Michael De Vlieger, <a href="/A325239/a325239_1.png">For m in row n, plot black else plot white</a>, n = 1..2^12.
%F A325239 A001222(T(n,k)) = A323023(n,k), n > 2, k <= A182850(n).
%e A325239 Triangle begins:
%e A325239    1              26 4 3 2        51 4 3 2          76 6 4 3 2
%e A325239    2              27 5 2          52 6 4 3 2        77 4 3 2
%e A325239    3 2            28 6 4 3 2      53 2              78 8 5 2
%e A325239    4 3 2          29 2            54 10 4 3 2       79 2
%e A325239    5 2            30 8 5 2        55 4 3 2          80 14 4 3 2
%e A325239    6 4 3 2        31 2            56 10 4 3 2       81 7 2
%e A325239    7 2            32 11 2         57 4 3 2          82 4 3 2
%e A325239    8 5 2          33 4 3 2        58 4 3 2          83 2
%e A325239    9 3 2          34 4 3 2        59 2              84 12 6 4 3 2
%e A325239   10 4 3 2        35 4 3 2        60 12 6 4 3 2     85 4 3 2
%e A325239   11 2            36 9 3 2        61 2              86 4 3 2
%e A325239   12 6 4 3 2      37 2            62 4 3 2          87 4 3 2
%e A325239   13 2            38 4 3 2        63 6 4 3 2        88 10 4 3 2
%e A325239   14 4 3 2        39 4 3 2        64 13 2           89 2
%e A325239   15 4 3 2        40 10 4 3 2     65 4 3 2          90 12 6 4 3 2
%e A325239   16 7 2          41 2            66 8 5 2          91 4 3 2
%e A325239   17 2            42 8 5 2        67 2              92 6 4 3 2
%e A325239   18 6 4 3 2      43 2            68 6 4 3 2        93 4 3 2
%e A325239   19 2            44 6 4 3 2      69 4 3 2          94 4 3 2
%e A325239   20 6 4 3 2      45 6 4 3 2      70 8 5 2          95 4 3 2
%e A325239   21 4 3 2        46 4 3 2        71 2              96 22 4 3 2
%e A325239   22 4 3 2        47 2            72 15 4 3 2       97 2
%e A325239   23 2            48 14 4 3 2     73 2              98 6 4 3 2
%e A325239   24 10 4 3 2     49 3 2          74 4 3 2          99 6 4 3 2
%e A325239   25 3 2          50 6 4 3 2      75 6 4 3 2       100 9 3 2
%t A325239 red[n_]:=Times@@Prime/@Last/@If[n==1,{},FactorInteger[n]];
%t A325239 Table[NestWhileList[red,n,#>2&],{n,30}]
%Y A325239 Row lengths are A182850(n) + 1.
%Y A325239 Cf. A001221, A001222, A071625, A118914, A181819, A181821, A182857, A323014, A323022, A323023, A325238, A325277.
%Y A325239 See A353510 for a full square array version of this table.
%K A325239 nonn,tabf
%O A325239 1,2
%A A325239 _Gus Wiseman_, Apr 15 2019