A304093 a(n) is the number of the proper divisors of n that are Lucas numbers (A000204, with 2 excluded).

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

Offset: 1

Author

Antti Karttunen, May 13 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A000204, A093540, A304091, A304094, A304095.

Cf. also A293435, A300836.

Programs

PARI

isA000204(n) = { my(u1=1,u2=3,old_u1); if(n<=2,(n%2),while(n>u2,old_u1=u1;u1=u2;u2=old_u1+u2);(u2==n)); };
A304093(n) = sumdiv(n,d,(dA000204(d));

Formula

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