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

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, 18, 8, 20, 10, 20, 14, 14, 20, 10, 20, 22, 22, 12, 16, 22, 16, 12, 22, 22, 10, 24, 24, 8, 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

Offset: 1

Author

Fred Daniel Kline, Jul 15 2018

Keywords

• nonn
• tabl

Comments

The greatest number in row k is 2*k + 4, thus consecutive rows identify consecutive even numbers (sums of primes).

To get the n-th row: copy (1...n) of A076565, reverse, and add together.

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.)

Examples

			{ 6},           <--- copy (1,1) of A076565, add together
{ 8,  8},       <--- copy (1,2) of A076565, reverse, and add together
{10, 10, 10},   <--- copy (1,3) of A076565, reverse, and add together
{ 6, 12, 12,  6},
{14,  8, 14,  8, 14},
{16, 16, 10, 10, 16, 16},
{ 8, 18, 18,  6, 18, 18,  8}, <=== differences with A316858 begin here
{20, 10, 20, 14, 14, 20, 10, 20},
{22, 22, 12, 16, 22, 16, 12, 22, 22},
{10, 24, 24,  8, 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}
		

Crossrefs

Cf. A076565, A316858 related triangle using lpfs.

Programs

Mathematica

gpf[n_] := FactorInteger[2 n + 1][[-1, 1]]; A076565 = Array[gpf, 12];
a = Table[A076565[[1 ;; -n]] + Reverse[A076565[[1 ;; -n]]],
  {n, Length[A076565], 1, -1}];