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A302787 a(1) = 0; for n > 1, a(n) = A000265(A052331(n)).

%I A302787 #9 Apr 16 2018 22:10:58
%S A302787 0,1,1,1,1,3,1,5,1,9,1,3,1,17,5,1,1,33,1,3,9,65,1,7,1,129,17,5,1,11,1,
%T A302787 257,33,513,3,9,1,1025,65,13,1,19,1,17,5,2049,1,129,1,4097,257,33,1,
%U A302787 35,9,21,513,8193,1,7,1,16385,3,65,17,67,1,129,1025,25,1,37,1,32769,2049,257,5,131,1,33,1,65537,1,11,65,131073,4097,69,1,41,9
%N A302787 a(1) = 0; for n > 1, a(n) = A000265(A052331(n)).
%C A302787 After n=1, differs from A240535 (which gives the same terms, but with mirrored binary expansion) for the first time at n=30, where a(30) = 11, while A240535(30) = 13. Note how 11 = "1011" and 13 = "1101" in binary.
%C A302787 For all i, j: a(i) = a(j) => A302791(i) = A302791(j).
%H A302787 Antti Karttunen, <a href="/A302787/b302787.txt">Table of n, a(n) for n = 1..8192</a>
%F A302787 a(1) = 0; for n > 1, a(n) = A000265(A052331(n)).
%F A302787 For n > 1, a(n) = A030101(A240535(n)).
%F A302787 For n >= 1, A069010(a(n)) = A302790(n).
%o A302787 (PARI)
%o A302787 up_to = 8192;
%o A302787 v050376 = vector(up_to);
%o A302787 ispow2(n) = (n && !bitand(n,n-1));
%o A302787 i = 0; for(n=1,oo,if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to,break));
%o A302787 A052331(n) = { my(s=0,e); while(n > 1, fordiv(n, d, if(((n/d)>1)&&ispow2(isprimepower(n/d)), e = vecsearch(v050376, n/d); if(!e, print("v050376 too short!"); return(1/0)); s += 2^(e-1); n = d; break))); (s); };
%o A302787 A000265(n) = (n/2^valuation(n, 2));
%o A302787 A302787(n) = if(1==n,0,A000265(A052331(n)));
%Y A302787 Cf. A000265, A050376, A052331, A240535, A302786, A302788, A302789, A302790, A302791.
%Y A302787 Cf. also A246277.
%K A302787 nonn
%O A302787 1,6
%A A302787 _Antti Karttunen_, Apr 13 2018