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

1,2

Comments

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

Links

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

Formula

Row n is row n of A027746 in reverse order.

Example

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

Prog

(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

Crossrefs

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

A001414 gives row sums (for n > 1).

Cf. A027746, A238690.

Sequence in context: A307746 A348477 A240230 * A166454 A283239 A318177

Adjacent sequences: A238686 A238687 A238688 * A238690 A238691 A238692

Keyword

nonn,tabf

Author

Matthew Vandermast, Apr 28 2014

Status

approved