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A316859 Triangle read by rows constructed from A076565 as sum of greatest prime factors.

%I A316859 #20 Jul 15 2018 12:56:32
%S A316859 6,8,8,10,10,10,6,12,12,6,14,8,14,8,14,16,16,10,10,16,16,8,18,18,6,18,
%T A316859 18,8,20,10,20,14,14,20,10,20,22,22,12,16,22,16,12,22,22,10,24,24,8,
%U A316859 24,24,8,24,24,10,26,12,26,20,16,26,16,20,26,12,26,8,28,14,22,28,18,18,28,22,14,28,8
%N A316859 Triangle read by rows constructed from A076565 as sum of greatest prime factors.
%C A316859 The greatest number in row k is 2*k + 4, thus consecutive rows identify consecutive even numbers (sums of primes).
%C A316859 To get the n-th row: copy (1...n) of A076565, reverse, and add together.
%C A316859 When primes meet primes we get the maximum values. When primes or prime factors meet prime factors, we get lesser values. (Spot checked. Still empirical.)
%e A316859 { 6},           <--- copy (1,1) of A076565, add together
%e A316859 { 8,  8},       <--- copy (1,2) of A076565, reverse, and add together
%e A316859 {10, 10, 10},   <--- copy (1,3) of A076565, reverse, and add together
%e A316859 { 6, 12, 12,  6},
%e A316859 {14,  8, 14,  8, 14},
%e A316859 {16, 16, 10, 10, 16, 16},
%e A316859 { 8, 18, 18,  6, 18, 18,  8}, <=== differences with A316858 begin here
%e A316859 {20, 10, 20, 14, 14, 20, 10, 20},
%e A316859 {22, 22, 12, 16, 22, 16, 12, 22, 22},
%e A316859 {10, 24, 24,  8, 24, 24,  8, 24, 24, 10},
%e A316859 {26, 12, 26, 20, 16, 26, 16, 20, 26, 12, 26},
%e A316859 { 8, 28, 14, 22, 28, 18, 18, 28, 22, 14, 28,  8}
%t A316859 gpf[n_] := FactorInteger[2 n + 1][[-1, 1]]; A076565 = Array[gpf, 12];
%t A316859 a = Table[A076565[[1 ;; -n]] + Reverse[A076565[[1 ;; -n]]],
%t A316859   {n, Length[A076565], 1, -1}];
%Y A316859 Cf. A076565, A316858 related triangle using lpfs.
%K A316859 nonn,tabl
%O A316859 1,1
%A A316859 _Fred Daniel Kline_, Jul 15 2018