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

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 *)

Prog

(PARI)
A102460(n) = { my(u1=1, u2=3, old_u1); if(n<=2, sign(n), while(n>u2, old_u1=u1; u1=u2; u2=old_u1+u2); (u2==n)); };
A304092(n) = sumdiv(n, d, A102460(d));

Crossrefs

Cf. A000032, A093540, A102460, A304091, A304094, A304096.

Cf. also A005086, A300837.

Sequence in context: A144911 A233431 A160650 * A339669 A171691 A088904

Adjacent sequences: A304089 A304090 A304091 * A304093 A304094 A304095

Keyword

nonn

Author

Antti Karttunen, May 13 2018

Status

approved