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

1,3

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

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 *)

Prog

(PARI) isA374122 = A374121;

Crossrefs

Cf. A328845, A374121 (characteristic function).

Cf. also A374046, A374052.

Sequence in context: A154967 A271211 A341044 * A072381 A046415 A358674

Adjacent sequences: A374119 A374120 A374121 * A374123 A374124 A374125

Keyword

nonn

Author

Antti Karttunen, Jun 28 2024

Status

approved