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A295298 Numbers n for which sum of the divisors (A000203) and the binary weight of n (A000120) have the same parity.

%I A295298 #19 Dec 02 2017 21:55:25
%S A295298 1,2,3,4,5,6,8,10,12,15,16,17,20,23,24,25,27,29,30,32,33,34,39,40,43,
%T A295298 45,46,48,49,50,51,53,54,57,58,60,63,64,65,66,68,71,75,77,78,80,81,83,
%U A295298 85,86,89,90,92,95,96,98,99,100,101,102,105,106,108,111,113,114,116,119,120,121,123,125,126,128,129,130,132,135,136
%N A295298 Numbers n for which sum of the divisors (A000203) and the binary weight of n (A000120) have the same parity.
%C A295298 Numbers n for which A010060(n) = A053866(n).
%C A295298 This sequence is the union of all terms of A028982 (squares and twice squares) that are odious (A000069), and all evil numbers (A001969) that are neither a square or twice a square. See also A231431, A235001.
%C A295298 Sequence A003401 is a subsequence of this sequence. This follows because the only terms in A003401 that are squares or twice squares are the powers of 2 (A000079, that have just one 1-bit, thus are odious), while all the other terms (obtained by multiplying distinct Fermat primes possibly with some power of 2) have an even number of 1-bits, and certainly cannot be squares nor twice squares. - _Antti Karttunen_, Nov 27 2017
%H A295298 Antti Karttunen, <a href="/A295298/b295298.txt">Table of n, a(n) for n = 1..10000</a>
%H A295298 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%t A295298 Select[Range@ 136, SameQ @@ Map[EvenQ, {DivisorSigma[1, #], DigitCount[#, 2, 1]}] &] (* _Michael De Vlieger_, Nov 26 2017 *)
%Y A295298 Positions of zeros in A295297.
%Y A295298 Complement of A295299.
%Y A295298 Cf. A000069, A001969, A000120, A000230, A010060, A028982, A053866, A231431, A235001.
%Y A295298 Cf. A000079, A003401, A295296 (subsequences), also A191363 (the five known terms).
%K A295298 nonn
%O A295298 1,2
%A A295298 _Antti Karttunen_, Nov 26 2017