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A304096
Number of Lucas numbers larger than 3 (4, 7, 11, 18, ...) that divide n.
6
0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 1, 0, 1, 2, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 1, 1
OFFSET
1,28
COMMENTS
a(n) is the number of the divisors d of n that are of the form d = A000045(k-1) + A000045(k+1), for k >= 3.
LINKS
FORMULA
a(n) = Sum_{d|n, d>3} A102460(d).
a(n) = A304094(n) - A079978(n) - 1.
a(n) = A304092(n) - A059841(n) - A079978(n) - 1.
a(n) = A007949(A304104(n)).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A093540 - 4/3 = 0.629524... . - Amiram Eldar, Dec 31 2023
EXAMPLE
The divisors of 4 are 1, 2 and 4. Of these only 4 is a Lucas number larger than 3, thus a(4) = 1.
The divisors of 28 are 1, 2, 4, 7, 14 and 28. Of these 4 and 7 are Lucas numbers (A000032) larger than 3, thus a(28) = 2.
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)); };
A304096(n) = sumdiv(n, d, (d>3)*A102460(d));
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 13 2018
STATUS
approved