A374046 Numbers k for which A328845(k) is even, where A328845 is the first Fibonacci based variant of arithmetic derivative.

0, 1, 3, 4, 8, 9, 12, 16, 20, 24, 25, 27, 28, 32, 35, 36, 40, 44, 48, 49, 52, 55, 56, 60, 64, 65, 68, 72, 75, 76, 77, 80, 81, 84, 85, 88, 91, 92, 95, 96, 100, 104, 105, 108, 112, 115, 116, 119, 120, 121, 124, 128, 132, 133, 136, 140, 143, 144, 145, 147, 148, 152, 155, 156, 160, 161, 164, 165, 168, 169, 172, 176, 180

Offset: 1

Author

Antti Karttunen, Jun 27 2024

Keywords

• nonn

Comments

A multiplicative semigroup: if m and n are in the sequence, then so is m*n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12000

Crossrefs

Cf. A328845, A374045 (characteristic function), A374047 (complement).

Cf. also A373586 (positions of even terms in A113177).

Programs

Mathematica

A374046Q[k_] := If[k <= 1, True, EvenQ[k*Total[MapApply[#2*Fibonacci[#]/# &, FactorInteger[k]]]]];
Select[Range[0, 200], A374046Q] (* Paolo Xausa, Dec 16 2024 *)

PARI

isA374046 = A374045;