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

1,3

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..20000

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 *)

Prog

(PARI) is_A379116 = A379117;

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.

Sequence in context: A313361 A059324 A112776 * A313362 A120063 A313363

Adjacent sequences: A379113 A379114 A379115 * A379117 A379118 A379119

Keyword

nonn

Author

Antti Karttunen, Dec 15 2024

Status

approved