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A034748 Dirichlet convolution of Fibonacci numbers with phi(n). 2
1, 2, 4, 6, 9, 14, 19, 30, 44, 68, 99, 168, 245, 402, 636, 1026, 1613, 2650, 4199, 6854, 10996, 17820, 28679, 46596, 75065, 121650, 196516, 318250, 514257, 832826, 1346299, 2179374, 3524796, 5704516, 9227571, 14933352, 24157853, 39092386 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..2000 (first 300 terms from Paolo P. Lava)

FORMULA

From definition a(n) = Sum_{d|n} F(d)*phi(n/d); also a(n) = Sum_{k=1..n} gcd(F(k), F(k+n)) where F(k) denotes the k-th Fibonacci number. - Benoit Cloitre, May 25 2003

G.f.: Sum_{k>=1} phi(k) * x^k/(1 - x^k - x^(2*k)). - Ilya Gutkovskiy, Jul 23 2019

a(n) ~ phi^n / sqrt(5), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jul 23 2019

MATHEMATICA

Table[Sum[Fibonacci[d] EulerPhi[n/d], {d, Divisors[n]}], {n, 1, 50}] (* Vincenzo Librandi, Aug 19 2018 *)

PROG

(PARI) a(n)=sumdiv(n, d, fibonacci(d)*eulerphi(n/d))

(MAGMA) [&+[Fibonacci(d)*EulerPhi(n div d): d in Divisors(n)]: n in [1..50]]; // Vincenzo Librandi, Aug 19 2018

CROSSREFS

Cf. A000010, A000045.

Sequence in context: A003402 A328863 A218004 * A069916 A153140 A295341

Adjacent sequences:  A034745 A034746 A034747 * A034749 A034750 A034751

KEYWORD

nonn

AUTHOR

Erich Friedman

STATUS

approved

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)