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

Author

Antti Karttunen, Nov 26 2017

Keywords

• nonn

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

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).

Programs

Mathematica

Select[Range@ 136, SameQ @@ Map[EvenQ, {DivisorSigma[1, #], DigitCount[#, 2, 1]}] &] (* Michael De Vlieger, Nov 26 2017 *)