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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.
8
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, 45, 46, 48, 49, 50, 51, 53, 54, 57, 58, 60, 63, 64, 65, 66, 68, 71, 75, 77, 78, 80, 81, 83, 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
OFFSET
1,2
COMMENTS
Numbers n for which A010060(n) = A053866(n).
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.
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
MATHEMATICA
Select[Range@ 136, SameQ @@ Map[EvenQ, {DivisorSigma[1, #], DigitCount[#, 2, 1]}] &] (* Michael De Vlieger, Nov 26 2017 *)
CROSSREFS
Positions of zeros in A295297.
Complement of A295299.
Cf. A000079, A003401, A295296 (subsequences), also A191363 (the five known terms).
Sequence in context: A204580 A347831 A331206 * A003401 A281624 A242441
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 26 2017
STATUS
approved