A295299 Numbers k such that the sum of the divisors (A000203) and the binary weight of k (A000120) have different parity.

7, 9, 11, 13, 14, 18, 19, 21, 22, 26, 28, 31, 35, 36, 37, 38, 41, 42, 44, 47, 52, 55, 56, 59, 61, 62, 67, 69, 70, 72, 73, 74, 76, 79, 82, 84, 87, 88, 91, 93, 94, 97, 103, 104, 107, 109, 110, 112, 115, 117, 118, 122, 124, 127, 131, 133, 134, 137, 138, 140, 143, 144, 145, 146, 148, 151, 152, 155, 157, 158, 161, 164, 167, 168, 169

Offset: 1

Author

Antti Karttunen, Nov 26 2017

Keywords

• nonn

Comments

Numbers k for which A010059(k) = A053866(k).

This sequence is the union of all terms of A028982 (squares and twice squares) that are evil (A001969), and all odious numbers (A000069) that are neither a square or twice a square. See also A231431, A235001.

This is a subsequence of A004169, numbers k such that phi(k) is not a power of 2. See comment in A295298 for the reason. - 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

Complement of A295298.

Subsequence of A004169.

Cf. A000069, A001969, A000120, A000203, A010059, A028982, A053866, A231431, A235001, A295297 (characteristic function).

Programs

Mathematica

Select[Range@ 169, UnsameQ @@ Map[EvenQ, {DivisorSigma[1, #], DigitCount[#, 2, 1]}] &] (* Michael De Vlieger, Nov 26 2017 *)