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A295298
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Numbers n for which sum of the divisors (A000203) and the binary weight of n (A000120) have the same parity.
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8
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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MATHEMATICA
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Select[Range@ 136, SameQ @@ Map[EvenQ, {DivisorSigma[1, #], DigitCount[#, 2, 1]}] &] (* Michael De Vlieger, Nov 26 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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