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

1,1

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.)

Links

Table of n, a(n) for n=1..78.

Example

{ 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}

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}];

Crossrefs

Cf. A076565, A316858 related triangle using lpfs.

Sequence in context: A113697 A154476 A316858 * A185200 A216275 A315946

Adjacent sequences: A316856 A316857 A316858 * A316860 A316861 A316862

Keyword

nonn,tabl

Author

Fred Daniel Kline, Jul 15 2018

Status

approved