A238689 Table read by rows: first row is {1}; for n >1, T(n, k) is the k-th largest prime factor of n (repeated prime factors are counted repeatedly).

1, 2, 3, 2, 2, 5, 3, 2, 7, 2, 2, 2, 3, 3, 5, 2, 11, 3, 2, 2, 13, 7, 2, 5, 3, 2, 2, 2, 2, 17, 3, 3, 2, 19, 5, 2, 2, 7, 3, 11, 2, 23, 3, 2, 2, 2, 5, 5, 13, 2, 3, 3, 3, 7, 2, 2, 29, 5, 3, 2, 31, 2, 2, 2, 2, 2, 11, 3, 17, 2, 7, 5, 3, 3, 2, 2, 37, 19, 2, 13, 3, 5, 2, 2, 2

Offset: 1

Author

Matthew Vandermast, Apr 28 2014

Keywords

• nonn
• tabf

Comments

n-th row has length 1 if n = 1, A001222(n) if n > 1.

Examples

			Table begins:
1;
2;
3;
2,2;
5;
3,2;
7;
2,2,2;
3,3;
5,2;
...
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000

Crossrefs

First column is A006530; numbers along right boundary form A020639.

A001414 gives row sums (for n > 1).

Cf. A027746, A238690.

Programs

Haskell

a238689_row 1 = [1]
a238689_row n = a n [] a000040_list where
  a m factors ps@(p:ps')
    | m == 1         = factors
    | m `mod` p == 0 = a (m `div` p) (p : factors) ps
    | otherwise      = a m           factors       ps'
a   [] = [] -- Peter Kagey, Sep 15 2016

Formula

Row n is row n of A027746 in reverse order.