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A374470 a(n) = gcd(bigomega(n), A064547(n)), where A064547 is the count of 1-bits in the exponents of the prime factorization of n, and bigomega is the number of prime factors of n (with multiplicity).

%I A374470 #7 Jul 14 2024 15:16:08
%S A374470 0,1,1,1,1,2,1,1,1,2,1,1,1,2,2,1,1,1,1,1,2,2,1,1,1,2,1,1,1,3,1,1,2,2,
%T A374470 2,2,1,2,2,1,1,3,1,1,1,2,1,1,1,1,2,1,1,1,2,1,2,2,1,1,1,2,1,2,2,3,1,1,
%U A374470 2,3,1,1,1,2,1,1,2,3,1,1,1,2,1,1,2,2,2,1,1,1,2,1,2,2,2,3,1,1,1,2,1,3,1,1,3
%N A374470 a(n) = gcd(bigomega(n), A064547(n)), where A064547 is the count of 1-bits in the exponents of the prime factorization of n, and bigomega is the number of prime factors of n (with multiplicity).
%H A374470 Antti Karttunen, <a href="/A374470/b374470.txt">Table of n, a(n) for n = 1..100000</a>
%H A374470 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%o A374470 (PARI)
%o A374470 A064547(n) = { my(f = factor(n)[, 2]); sum(k=1, #f, hammingweight(f[k])); };
%o A374470 A374470(n) = gcd(bigomega(n),A064547(n));
%Y A374470 Cf. A001222, A064547, A374471, A374472 (indices of even terms), A374473 (of odd terms).
%Y A374470 Differs from A327500, A362613, A351946, A353507 first at n=60, where a(60) = 1.
%Y A374470 Differs from A362611 first at n=64, where a(64) = 2, while A362611(64) = 1.
%K A374470 nonn
%O A374470 1,6
%A A374470 _Antti Karttunen_, Jul 14 2024