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%I #17 Apr 22 2019 13:49:08
%S 1,1,2,1,3,0,2,1,1,2,2,3,3,3,2,1,5,1,2,2,2,4,2,3,1,2,2,0,3,3,2,1,2,2,
%T 2,1,3,5,2,2,4,3,2,3,3,3,2,3,1,1,2,2,3,3,2,4,2,2,2,4,3,3,2,1,2,3,2,2,
%U 2,3,2,1,4,2,2,3,2,3,2,2,1,2,2,6,2,4,2,3,4,2,2,5,2,3,2,3,6,1,2,1,3,3,2,2,2
%N a(n) = A001511(A325315(n)), except when A325315(n) = 0, then a(n) = 0.
%H Antti Karttunen, <a href="/A325310/b325310.txt">Table of n, a(n) for n = 1..65537</a>
%F If A325315(n) = 0, then a(n) = 0, otherwise a(n) = A001511(A325315(n)).
%F a(A228058(n)) = A001511(abs(A325379(n))), assuming there are no odd perfect numbers, in which case a(A228058(n)) >= 3 for all n.
%t Array[If[# == 0, 0, IntegerExponent[2 #, 2]] &[BitXor @@ Abs[#1 - Map[Total, {#3, Complement[#2, #3]}]]] & @@ {#1, #2, Select[#2, SquareFreeQ]} & @@ {#, Divisors[#]} &, 105] (* _Michael De Vlieger_, Apr 21 2019 *)
%o (PARI)
%o A001511ext(n) = if(!n,n,sign(n)*(1+valuation(n,2))); \\ Like A001511 but gives 0 for 0 and -A001511(-n) for negative numbers.
%o A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
%o A325313(n) = (A048250(n) - n);
%o A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
%o A325314(n) = (n - A162296(n));
%o A325315(n) = bitxor(abs(A325313(n)),abs(A325314(n)));
%o A325310(n) = A001511ext(A325315(n));
%Y Cf. A000396, A001511, A028982 (gives the positions of 1's), A048250, A162296, A228058, A325313, A325314, A325315, A325378, A325379.
%K nonn
%O 1,3
%A _Antti Karttunen_, Apr 21 2019
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