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A304092
Number of Lucas numbers (A000032: 2, 1, 3, 4, 7, 11, ...) dividing n.
9
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 13 2018
STATUS
approved