A270430 Numbers n such that A048673(n) and A064216(n) are of the same parity.

1, 2, 3, 4, 5, 8, 9, 10, 12, 13, 16, 17, 20, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 39, 40, 41, 42, 48, 49, 50, 52, 53, 58, 62, 64, 65, 68, 69, 74, 75, 77, 80, 81, 82, 85, 90, 93, 97, 98, 99, 100, 101, 102, 104, 105, 106, 108, 109, 111, 113, 114, 116, 117, 120, 121, 124, 125, 126, 128, 130, 132, 133, 136, 137, 139, 141, 144

Offset: 1

Author

Antti Karttunen, Mar 17 2016

Keywords

• nonn

Comments

See A270434 for the possible bias favoring this sequence over the complement A270431.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..17000

Crossrefs

Complement: A270431.

Left inverse: A270432.

Cf. A245449 (a subsequence).

Cf. A000035, A048673, A064216, A270434.

Cf. also A269860.

Programs

Mathematica

f[n_] := (Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ n; g[n_] := Times @@ Power[If[# == 1, 1, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger[2 n - 1]; Select[Range@ 144, Xor[EvenQ@ f@ #, OddQ@ g@ #] &] (* Michael De Vlieger, Mar 17 2016 *)

Formula

Other identities. For all n >= 1:

A270432(a(n)) = n.