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A064364 Positive integers sorted by A001414(n), the sum of their prime divisors, as the major key and n as the minor key. 7
1, 2, 3, 4, 5, 6, 8, 9, 7, 10, 12, 15, 16, 18, 14, 20, 24, 27, 21, 25, 30, 32, 36, 11, 28, 40, 45, 48, 54, 35, 42, 50, 60, 64, 72, 81, 13, 22, 56, 63, 75, 80, 90, 96, 108, 33, 49, 70, 84, 100, 120, 128, 135, 144, 162, 26, 44, 105, 112, 125, 126, 150, 160, 180, 192, 216, 243 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is a permutation of the positive integers.

a(1) could be taken as 0 because 1 is not a member of A001414 and one could start with a(0)=1 (see the W. Lang link).

The row length sequence of this array is A000607(n), n>=2.

If the array is [1,0,2,3,4,5,6,6,...] with offset 0 then the row length sequence is A000607(n), n>=0.

LINKS

Reinhard Zumkeller and Alois P. Heinz, Rows n = 1..60, flattened (first 32 rows from Reinhard Zumkeller)

W. Lang: First 16 rows.

H. Havermann: The first 100 sums (complete, a 6 MB file).

H. Havermann: Tables of sum-of-prime-factors sequences (overview with links to the first 50000 sums).

Index entries for sequences that are permutations of the natural numbers

EXAMPLE

The triangle reads:

1,

(0,) (see comment in link to "first 16 rows" by W. Lang)

2,

3,

4,

5,  6,

8,  9,

7,  10, 12,

15, 16, 18,

14, 20, 24, 27,

21, 25, 30, 32, 36,

11, 28, 40, 45, 48, 54,

35, 42, 50, 60, 64, 72, 81,

13, 22, 56, 63, 75, 80, 90, 96, 108,

...

PROG

(Haskell)

import Data.List (partition, union)

a064364 n k = a064364_tabf !! (n-1) !! (k-1)

a064364_row n = a064364_tabf !! (n-1)

a064364_tabf = [1] : tail (f 1 [] 1 (map a000792 [2..])) where

   f k pqs v (w:ws) = (map snd pqs') :

     f (k + 1) (union pqs'' (zip (map a001414 us) us )) w ws where

       us = [v + 1 .. w]

       (pqs', pqs'') = partition ((== k) . fst) pqs

a064364_list = concat a064364_tabf

-- Reinhard Zumkeller, Jun 11 2015

CROSSREFS

Cf. A001414.

Cf. A000607 (row lengths), A002098 (row sums), A056240 (least = first term in the n-th row), A000792 (greatest term in the n-th row).

Cf. A257815 (inverse).

Sequence in context: A097502 A265568 A265552 * A269855 A209274 A195184

Adjacent sequences:  A064361 A064362 A064363 * A064365 A064366 A064367

KEYWORD

easy,nonn,tabf

AUTHOR

Howard A. Landman, Sep 25 2001

EXTENSIONS

More terms from Vladeta Jovovic, Sep 27 2005

STATUS

approved

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Last modified November 20 10:41 EST 2017. Contains 294963 sequences.