A241911 After a(1)=1, numbers 1 .. bigomega(n), followed by numbers 1 .. bigomega(n+1), etc., where bigomega(n)=A001222(n) is the number of prime factors of n (with repetition).

1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 2, 1, 2, 3, 4, 1, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 2, 1, 1, 2, 3, 4, 1, 2, 1, 2, 1, 2, 3, 1, 2, 3, 1, 1, 2, 3, 1, 1, 2, 3, 4, 5, 1, 2, 1, 2, 1, 2, 1, 2, 3, 4, 1, 1, 2, 1, 2, 1, 2, 3, 4, 1, 1, 2, 3, 1, 1, 2, 3, 1, 2, 3, 1, 2, 1, 1, 2, 3, 4, 5, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 1, 2, 3, 4, 1

Offset

1,5

Links

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

Formula

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

Example

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

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define (A241911 n) (if (= n 1) 1 (- n (A022559 (- (A082288 n) 1)) 1)))

Crossrefs

One more than A241910.

Cf. A022559, A082288, A241915.

Sequence in context: A364137 A240061 A162320 * A335221 A136610 A377365

Adjacent sequences: A241908 A241909 A241910 * A241912 A241913 A241914

Keyword

nonn,tabf

Author

Antti Karttunen, May 01 2014

Status

approved