A070964 a(n) = Sum_{1<=k<=n, gcd(k,n)=1} Fibonacci(k).

1, 1, 2, 3, 7, 6, 20, 21, 44, 50, 143, 108, 376, 364, 738, 987, 2583, 1938, 6764, 6150, 13938, 17622, 46367, 34776, 113957, 121160, 257114, 306852, 832039, 549000, 2178308, 2178309, 4595932, 5701290, 13686704, 11197764, 39088168, 39083988, 82668444, 93031050, 267914295

Offset

1,3

Links

John Tyler Rascoe, Table of n, a(n) for n = 1..500

Example

The 12th term is F(1) + F(5) + F(7) + F(11) = 1 + 5 + 13 + 89 = 108, where F(n) is the n-th Fibonacci number and 1, 5, 7 and 11 are the positive integers <= 12 and relatively prime to 12.

Maple

a:= n-> add(`if`(igcd(k, n)>1, 0, combinat[fibonacci](k)), k=1..n):
seq(a(n), n=1..41);

Prog

(PARI)
A070964(n) = {sum(k=1, n, if(gcd(n, k)==1, fibonacci(k)))} \\ John Tyler Rascoe, Feb 03 2026

Crossrefs

Cf. A000045, A119737.

Sequence in context: A187015 A377270 A245467 * A111075 A011372 A104955

Adjacent sequences: A070961 A070962 A070963 * A070965 A070966 A070967

Keyword

nonn,easy

Author

Leroy Quet, May 16 2002

Status

approved