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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).

%I A241910 #9 May 15 2014 10:20:00
%S A241910 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,
%T A241910 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,
%U A241910 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
%N 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).
%H A241910 Antti Karttunen, <a href="/A241910/b241910.txt">Table of n, a(n) for n = 1..10000</a>
%F A241910 a(1)=0, a(n) = n - A022559(A082288(n)-1) - 2.
%e A241910 Viewed as an irregular table, the sequence is constructed as:
%e A241910 "Row"
%e A241910   [1] 0; (by convention, a(1)=0)
%e A241910   [2] 0; (because bigomega(2)=1, we have here terms from 0 to 0)
%e A241910   [3] 0; (same with 3, bigomega(3)=1)
%e A241910   [4] 0, 1; (as bigomega(4)=2, we have terms from 0 to 2-1)
%e A241910   [5] 0;
%e A241910   [6] 0, 1;
%e A241910   [7] 0;
%e A241910   [8] 0, 1, 2; (as bigomega(8)=3, we have terms from 0 to 3-1).
%e A241910 etc.
%o A241910 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A241910 (define (A241910 n) (if (= n 1) 0 (- n (+ 2 (A022559 (- (A082288 n) 1))))))
%Y A241910 One less than A241911.
%Y A241910 Cf. A022559, A082288, A112798, A241914.
%K A241910 nonn,tabf
%O A241910 1,12
%A A241910 _Antti Karttunen_, May 01 2014