A304092 - OEIS

A304092

Number of Lucas numbers (A000032: 2, 1, 3, 4, 7, 11, ...) dividing n.

1, 2, 2, 3, 1, 3, 2, 3, 2, 2, 2, 4, 1, 3, 2, 3, 1, 4, 1, 3, 3, 3, 1, 4, 1, 2, 2, 4, 2, 3, 1, 3, 3, 2, 2, 5, 1, 2, 2, 3, 1, 4, 1, 4, 2, 2, 2, 4, 2, 2, 2, 3, 1, 4, 2, 4, 2, 3, 1, 4, 1, 2, 3, 3, 1, 4, 1, 3, 2, 3, 1, 5, 1, 2, 2, 4, 3, 3, 1, 3, 2, 2, 1, 5, 1, 2, 3, 4, 1, 4, 2, 3, 2, 3, 1, 4, 1, 3, 3, 3, 1, 3, 1, 3, 3

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OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

a(n) = Sum_{d|n} A102460(d).

a(n) = A304091(n) + A102460(n).

a(n) = A304094(n) + A059841(n) = A304096(n) + A059841(n) + A079978(n) + 1.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A093540 + 1/2 = 2.462858... . - Amiram Eldar, Dec 31 2023

MATHEMATICA

Module[{nn=11, luc}, luc=LucasL[Range[0, nn]]; Table[Count[n/luc, _?IntegerQ], {n, Max[luc]}]] (* Harvey P. Dale, Jul 01 2023 *)