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A324912 Binary weight of A324911(n).

%I A324912 #6 Apr 14 2019 17:23:14
%S A324912 1,1,1,2,1,1,1,3,2,1,1,2,1,1,1,4,1,2,1,2,1,1,1,3,2,1,3,2,1,1,1,5,1,1,
%T A324912 1,2,1,1,1,3,1,1,1,2,2,1,1,4,2,2,1,2,1,3,1,3,1,1,1,2,1,1,2,6,1,1,1,2,
%U A324912 1,1,1,3,1,1,2,2,1,1,1,4,4,1,1,2,1,1,1,3,1,2,1,2,1,1,1,5,1,2,2,2,1,1,1,3,1
%N A324912 Binary weight of A324911(n).
%C A324912 After 1 differs from A051903 at n = 900, 1764, 1800, 2700, 3528, 4356, 4500, 4900, 5292, ..., which seems to be a subsequence of A318720.
%H A324912 Antti Karttunen, <a href="/A324912/b324912.txt">Table of n, a(n) for n = 1..65537</a>
%H A324912 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324912 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A324912 a(n) = A000120(A324911(n)).
%e A324912 For n = 900 = 2^2 * 3^2 * 5^2, A324911(900) = A156552(4) * A156552(9) * A156552(25) = 3*6*12 = 216, which in base-2 is written as "11011000", thus a(900) = 4.
%o A324912 (PARI)
%o A324912 A156552(n) = { my(f = factor(n), 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 A324912 A324911(n) = { my(f=factor(n)); prod(i=1, #f~, A156552(f[i,1]^f[i,2])); };
%o A324912 A324912(n) = hammingweight(A324911(n));
%Y A324912 Cf. A000120, A051903, A156552, A318720, A324911.
%Y A324912 Differs from A072411 for the first time at n=72, where a(72) = 3, while A072411(72) = 6.
%K A324912 nonn
%O A324912 1,4
%A A324912 _Antti Karttunen_, Apr 14 2019