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A322811 a(1) = 0; for n > 1, a(n) = A001221(A285330(n)).

%I A322811 #9 Dec 27 2018 17:35:46
%S A322811 0,0,1,1,1,1,1,1,1,1,1,2,1,1,2,1,1,2,1,2,2,1,1,2,1,2,1,2,1,1,1,1,2,2,
%T A322811 2,2,1,2,2,2,1,1,1,2,2,1,1,2,1,2,3,2,1,2,2,2,3,2,1,3,1,2,2,1,2,1,1,2,
%U A322811 3,1,1,2,1,2,2,2,2,2,1,2,1,2,1,3,2,2,2,2,1,3,2,2,3,3,3,2,1,2,2,2,1,1,1,2,2
%N A322811 a(1) = 0; for n > 1, a(n) = A001221(A285330(n)).
%C A322811 For all i, j:
%C A322811   A322806(i) = A322806(j) => a(i) = a(j),
%C A322811   A322807(i) = A322807(j) => a(i) = a(j).
%H A322811 Antti Karttunen, <a href="/A322811/b322811.txt">Table of n, a(n) for n = 1..10000</a>
%F A322811 a(1) = 0; for n > 1, a(n) = A001221(A285330(n)).
%F A322811 If n > 1 is squarefree, a(n) = A322812(n) = A001221(A048675(n)), otherwise a(n) = A001221(A285328(n)) = A001221(n).
%o A322811 (PARI)
%o A322811 A007947(n) = factorback(factorint(n)[, 1]); \\ From A007947
%o A322811 A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ From A048675
%o A322811 A285328(n) = { my(r); if((n > 1 && !bitand(n,(n-1))), (n/2), r=A007947(n); if(r==n,1,n = n-r; while(A007947(n) <> r, n = n-r); n)); };
%o A322811 A285330(n) = if(issquarefree(n),A048675(n),A285328(n));
%o A322811 A322811(n) = if(1==n,0,omega(A285330(n)));
%Y A322811 Cf. A001221, A048675, A285330, A322806, A322807, A322812.
%K A322811 nonn
%O A322811 1,12
%A A322811 _Antti Karttunen_, Dec 27 2018