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%I #7 Apr 06 2018 10:15:28
%S 0,1,1,1,1,2,1,1,1,2,1,2,1,2,2,1,1,2,1,2,1,2,1,2,1,2,2,2,1,3,1,1,2,2,
%T 2,2,1,2,2,2,1,2,1,2,1,2,1,2,1,2,2,2,1,3,1,2,2,2,2,3,1,2,2,1,2,3,1,2,
%U 2,3,1,2,1,2,2,2,1,3,2,2,2,2,1,2,1,2,3,2,1,2,1,2,1,2,2,2,1,2,2,2,1,3,2,2,2
%N An omega (A001221) analog based on the Ludic sieve (A255127): a(1) = 0; for n > 1, a(n) = 1 + a(A302034(n)).
%H Antti Karttunen, <a href="/A302031/b302031.txt">Table of n, a(n) for n = 1..32768</a>
%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%F a(1) = 0; for n > 1, a(n) = 1 + a(A302034(n)).
%F a(n) = A001221(A302026(n)).
%F a(n) = A069010(A269388(n)).
%o (PARI)
%o \\ Assuming that A269379 and A269380 have been precomputed:
%o A302034(n) = if(1==n,n,my(k=0); while((n%2), n = A269380(n); k++); n = (n/2^valuation(n, 2)); while(k>0, n = A269379(n); k--); (n));
%o A302031(n) = if(1==n,0,1+A302031(A302034(n)));
%Y Cf. A001221, A302026, A302037, A302041,
%Y Cf. A302036 (positions of terms < 2).
%Y Differs from similar A302041 for the first time at n=59, where a(59) = 2, while A302041(59) = 1.
%K nonn
%O 1,6
%A _Antti Karttunen_, Apr 02 2018
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