A249809 Irregular table read by rows: T(n, k) is the number of times prime p_k has occurred as the smallest prime factor of numbers 1 .. n. (T(1,1) = 0, and for each n > 1, k = 1 .. A000720(n)).

0, 1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 4, 2, 1, 1, 5, 2, 1, 1, 5, 2, 1, 1, 1, 6, 2, 1, 1, 1, 6, 2, 1, 1, 1, 1, 7, 2, 1, 1, 1, 1, 7, 3, 1, 1, 1, 1, 8, 3, 1, 1, 1, 1, 8, 3, 1, 1, 1, 1, 1, 9, 3, 1, 1, 1, 1, 1, 9, 3, 1, 1, 1, 1, 1, 1, 10, 3, 1, 1, 1, 1, 1, 1, 10, 4, 1, 1, 1, 1, 1, 1, 11, 4, 1, 1, 1, 1, 1, 1, 11, 4, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Antti Karttunen, Nov 06 2014

Keywords

• nonn
• tabf

Comments

After the first row {0}, consists of rows of triangular table A249808 with trailing zeros removed.

Examples

			Table begins:
       k=1  2  3  4  5  6  7
  n=1:   0;
  n=2:   1;
  n=3:   1, 1;
  n=4:   2, 1;
  n=5:   2, 1, 1;
  n=6:   3, 1, 1;
  n=7:   3, 1, 1, 1;
  n=8:   4, 1, 1, 1;
  n=9:   4, 2, 1, 1;
  n=10:  5, 2, 1, 1;
  n=11:  5, 2, 1, 1, 1;
  n=12:  6, 2, 1, 1, 1;
  n=13:  6, 2, 1, 1, 1, 1;
  n=14:  7, 2, 1, 1, 1, 1;
  n=15:  7, 3, 1, 1, 1, 1;
  n=16:  8, 3, 1, 1, 1, 1;
  n=17:  8, 3, 1, 1, 1, 1, 1;
  ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10016; the first 294 rows of the table, flattened
• Orges Leka, Fractal of prime factorization of integers, lexicographically sorted.
• Orges Leka, How to define a fractal from the lexicographic sorting on the prime factorization of natural numbers?

Crossrefs

A004526 gives the left edge, A001477 the row sums.

Cf. A000040, A000720, A020639, A249808, A249727, A249728, A055396, A078898.

Programs

Scheme

(define (A249809 n) (A249808bi (A249728 n) (A249727 n))) ;; Code for A249808bi given in A249808.

Formula

a(n) = A249808(A249728(n), A249727(n)).

For n > 1, A078898(n) = T(n, A055396(n)).