A270431 Numbers n such that A048673(n) and A064216(n) are of opposite parity.

6, 7, 11, 14, 15, 18, 19, 21, 22, 23, 24, 28, 35, 38, 43, 44, 45, 46, 47, 51, 54, 55, 56, 57, 59, 60, 61, 63, 66, 67, 70, 71, 72, 73, 76, 78, 79, 83, 84, 86, 87, 88, 89, 91, 92, 94, 95, 96, 103, 107, 110, 112, 115, 118, 119, 122, 123, 127, 129, 131, 134, 135, 138, 140, 142, 143, 146, 150, 152, 153, 157, 158, 159, 162

Offset: 1

Author

Antti Karttunen, Mar 17 2016

Keywords

• nonn

Comments

See comments in A270434.

Links

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

Crossrefs

Complement: A270430.

Left inverse: A270433.

Cf. A000035, A048673, A064216, A270434.

Cf. also A269861.

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@ 162, Xor[EvenQ@ f@ #, EvenQ@ g@ #] &] (* Michael De Vlieger, Mar 17 2016 *)

Formula

Other identities. For all n >= 1:

A270433(a(n)) = n.