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

1,5

Comments

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

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?

Formula

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

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

Example

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;
  ...

Prog

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

Crossrefs

A004526 gives the left edge, A001477 the row sums.

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

Sequence in context: A361462 A129479 A261095 * A075104 A253667 A360189

Adjacent sequences: A249806 A249807 A249808 * A249810 A249811 A249812

Keyword

nonn,tabf,changed

Author

Antti Karttunen, Nov 06 2014

Status

approved