A374122 Numbers k for which A328845(k) is a multiple of 3, where A328845 is the first Fibonacci-based variant of the arithmetic derivative.

0, 1, 8, 9, 10, 14, 18, 22, 27, 36, 45, 52, 54, 58, 62, 63, 64, 65, 68, 72, 76, 80, 81, 85, 90, 91, 92, 95, 99, 100, 106, 108, 112, 115, 117, 118, 119, 125, 126, 133, 135, 140, 143, 144, 146, 148, 153, 158, 161, 162, 164, 166, 171, 172, 175, 176, 180, 185, 187, 188, 189, 194, 196, 198, 202, 205, 206, 207, 209, 214, 215

Offset: 1

Author

Antti Karttunen, Jun 28 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, A374121 (characteristic function).

Cf. also A374046, A374052.

Programs

Mathematica

A374122Q[k_] := If[k <= 1, True, Divisible[k*Total[MapApply[#2*Fibonacci[#]/# &, FactorInteger[k]]], 3]];
Select[Range[0, 300], A374122Q] (* Paolo Xausa, Dec 16 2024 *)

PARI

isA374122 = A374121;