A379116 Numbers k for which A328845(k) is a multiple of 5, where A328845 is the first Fibonacci based variant of arithmetic derivative.

0, 1, 5, 10, 12, 15, 20, 25, 28, 30, 32, 35, 39, 40, 44, 45, 50, 51, 54, 55, 60, 65, 70, 75, 76, 80, 85, 87, 90, 91, 92, 95, 100, 104, 105, 110, 111, 115, 119, 120, 123, 124, 125, 126, 130, 135, 136, 140, 143, 144, 145, 150, 155, 159, 160, 165, 170, 172, 175, 180, 183, 185, 187, 188, 190, 195, 198, 200, 203, 205

Offset: 1

Author

Antti Karttunen, Dec 15 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..20000

Crossrefs

Positions of multiples of 5 in A328845, of nonzero terms in A374205, of 0's in A379115.

Cf. A379117 (characteristic function).

Cf. also A374046, A374122.

Programs

Mathematica

A379116Q[k_] := If[k <= 1, True, Divisible[k*Total[MapApply[#2*Fibonacci[#]/# &, FactorInteger[k]]], 5]];
Select[Range[0, 300], A379116Q] (* Paolo Xausa, Dec 16 2024 *)

PARI

is_A379116 = A379117;