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