A241910 After a(1)=0, numbers 0 .. bigomega(n)-1, followed by numbers 0 .. bigomega(n+1)-1, etc., where bigomega(n)=A001222(n) is the number of prime factors of n (with repetition).

0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 1, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 1, 0, 1, 2, 3, 0, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 0, 0, 1, 2, 3, 0, 1, 0, 1, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 2, 3, 4, 0, 1, 0, 1, 0, 1, 0, 1, 2, 3, 0, 0, 1, 0, 1, 0, 1, 2, 3, 0, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 1, 0, 0, 1, 2, 3, 4, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 2, 3, 0

Offset

1,12

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(1)=0, a(n) = n - A022559(A082288(n)-1) - 2.

Example

Viewed as an irregular table, the sequence is constructed as:
"Row"
  [1] 0; (by convention, a(1)=0)
  [2] 0; (because bigomega(2)=1, we have here terms from 0 to 0)
  [3] 0; (same with 3, bigomega(3)=1)
  [4] 0, 1; (as bigomega(4)=2, we have terms from 0 to 2-1)
  [5] 0;
  [6] 0, 1;
  [7] 0;
  [8] 0, 1, 2; (as bigomega(8)=3, we have terms from 0 to 3-1).
etc.

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define (A241910 n) (if (= n 1) 0 (- n (+ 2 (A022559 (- (A082288 n) 1))))))

Crossrefs

One less than A241911.

Cf. A022559, A082288, A112798, A241914.

Sequence in context: A070095 A060951 A115525 * A065717 A070092 A365545

Adjacent sequences: A241907 A241908 A241909 * A241911 A241912 A241913

Keyword

nonn,tabf

Author

Antti Karttunen, May 01 2014

Status

approved