A316858 -id:A316858 - cp's OEIS frontend

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

Fred Daniel Kline, Jul 15 2018

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.)

			{ 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}

Cf. A076565, A316858 related triangle using lpfs.

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}];

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica