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A364570 a(n) = A252464(n) - A364569(n), where A364569(n) is the length of the common prefix in the binary expansions of A156552(n) and n-1 [= A156552(A005940(n))].

%I A364570 #10 Aug 14 2023 19:50:48
%S A364570 0,0,0,0,0,0,3,0,2,0,3,0,5,4,3,0,2,3,5,0,3,4,7,0,0,6,2,5,9,4,10,0,2,3,
%T A364570 3,4,9,6,4,0,11,4,12,5,0,8,13,0,0,1,7,7,15,3,5,6,8,10,16,5,17,11,5,0,
%U A364570 3,3,14,4,6,4,16,5,18,10,4,7,4,5,19,0,4,12,21,5,6,13,9,6,22,1,5,9,10,14,7,0,24,1,6
%N A364570 a(n) = A252464(n) - A364569(n), where A364569(n) is the length of the common prefix in the binary expansions of A156552(n) and n-1 [= A156552(A005940(n))].
%H A364570 Antti Karttunen, <a href="/A364570/b364570.txt">Table of n, a(n) for n = 1..65537</a>
%o A364570 (PARI)
%o A364570 Abincompreflen(n, m) = { my(x=binary(n), y=binary(m), u=min(#x, #y)); for(i=1, u, if(x[i]!=y[i], return(i-1))); (u); };
%o A364570 A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
%o A364570 A364569(n) = Abincompreflen(A156552(n), (n-1));
%o A364570 A061395(n) = if(n>1, primepi(vecmax(factor(n)[, 1])), 0);
%o A364570 A252464(n) = if(1==n,0,(bigomega(n) + A061395(n) - 1));
%o A364570 A364570(n) = (A252464(n)-A364569(n));
%Y A364570 Cf. A005940, A156552, A252464, A364569, A364570, A364960 (positions of 0's).
%Y A364570 Cf. also A347381.
%K A364570 nonn
%O A364570 1,7
%A A364570 _Antti Karttunen_, Aug 14 2023