A304091 - OEIS

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

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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).

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));