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Number of irreducible factors (counted with multiplicity) of the (0,1)-polynomial encoded in the binary expansion of n has when it is factored over Q.
1

%I #9 Jun 10 2018 21:15:35

%S 0,1,1,2,1,2,1,3,2,2,1,3,1,2,2,4,1,3,1,3,2,2,1,4,1,2,3,3,1,3,1,5,2,2,

%T 2,4,1,2,2,4,1,3,1,3,3,2,1,5,2,2,2,3,1,4,1,4,2,2,1,4,1,2,3,6,2,3,1,3,

%U 1,3,1,5,1,2,3,3,1,3,1,5,1,2,1,4,2,2,1,4,1,4,1,3,2,2,2,6,1,3,3,3,1,3,1,4,3

%N Number of irreducible factors (counted with multiplicity) of the (0,1)-polynomial encoded in the binary expansion of n has when it is factored over Q.

%H Antti Karttunen, <a href="/A305822/b305822.txt">Table of n, a(n) for n = 1..65537</a>

%F For all n >= 1, a(n) >= A206719(n).

%o (PARI) A305822(n) = vecsum(factor(Pol(binary(n)))[, 2]);

%Y Cf. A206074 (gives the positions of 1's), A206719, A257000, A304751.

%Y Cf. also A001222, A091222.

%Y Differs from A277013 for the first time at n=65, where a(65) = 2, while A277013(65) = 1.

%K nonn

%O 1,4

%A _Antti Karttunen_, Jun 10 2018