A304091 a(n) is the number of the proper divisors of n that are Lucas numbers (A000032, with 2 included).

0, 1, 1, 2, 1, 3, 1, 3, 2, 2, 1, 4, 1, 3, 2, 3, 1, 3, 1, 3, 3, 3, 1, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 2, 5, 1, 2, 2, 3, 1, 4, 1, 4, 2, 2, 1, 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, 3, 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

1,4

Links

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

Formula

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

a(n) = A304092(n) - A102460(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/2 + A093540 = 2.462858... . - Amiram Eldar, Jul 05 2025

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)); };
A304091(n) = sumdiv(n, d, (d<n)*A102460(d));

Crossrefs

Cf. A000032, A093540, A102460, A304092, A304093.

Cf. also A293435, A300836.

Sequence in context: A345063 A337216 A249617 * A278801 A307720 A191350

Adjacent sequences: A304088 A304089 A304090 * A304092 A304093 A304094

Keyword

nonn

Author

Antti Karttunen, May 13 2018

Status

approved