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

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n

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. A000069, A001969, A000120, A000230, A010060, A028982, A053866, A231431, A235001.

Cf. A000079, A003401, A295296 (subsequences), also A191363 (the five known terms).

Sequence in context: A204580 A347831 A331206 * A003401 A281624 A242441

Adjacent sequences: A295295 A295296 A295297 * A295299 A295300 A295301

Keyword

nonn

Author

Antti Karttunen, Nov 26 2017

Status

approved