A241911 -id:A241911 - cp's OEIS frontend

A241915 After a(1)=1, numbers 1 .. A061395(n), followed by numbers 1 .. A061395(n+1), etc.

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

Offset: 1

Antti Karttunen, May 01 2014

			Viewed as an irregular table, the sequence is constructed as:
"Row"
  [1] 1; (by convention, a(1)=1)
  [2] 1; (because A061395(2)=1 (the index of the largest prime factor), we have here terms from 1 to 1)
  [3] 1, 2; (because A061395(3)=2, we have terms from 1 to 2)
  [4] 1;
  [5] 1, 2, 3; (because A061395(5)=3, we have terms from 1 to 3)
  [6] 1, 2;    (because A061395(6)=2, we have terms from 1 to 2)
  [7] 1, 2, 3, 4; (because A061395(7)=4, we have terms from 1 to 4)
etc.

Antti Karttunen, Table of n, a(n) for n = 1..10082

One more than A241914.

Cf. A203623, A241920, A241911.

(define (A241915 n) (if (= n 1) 1 (- n (A203623 (- (A241920 n) 1)) 1)))

a(1)=1, a(n) = n - A203623(A241920(n)-1) - 1.

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).

Original entry on oeis.org

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

Antti Karttunen, May 01 2014

			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.

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

One less than A241911.

Cf. A022559, A082288, A112798, A241914.

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

cp's OEIS Frontend

A241915 After a(1)=1, numbers 1 .. A061395(n), followed by numbers 1 .. A061395(n+1), etc.

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