%I #28 Dec 24 2022 03:49:11
%S 1,2,3,4,5,6,8,8,9,10,13,12,21,16,15,16,34,18,55,20,24,26,89,24,25,42,
%T 27,32,144,30,233,32,39,68,40,36,377,110,63,40,610,48,987,52,45,178,
%U 1597,48,64,50,102,84,2584,54,65,64,165,288,4181,60,6765,466,72,64,105,78,10946
%N Fully multiplicative with a(prime(k)) = Fibonacci(k+2).
%C Numbers k such that a(k) = k are exactly 5-smooth numbers (A051037). - _Ivan Neretin_, Aug 30 2015
%H Ivan Neretin, <a href="/A003965/b003965.txt">Table of n, a(n) for n = 1..10000</a>
%F If n = Product p(k)^e(k) then a(n) = Product Fibonacci(k+2)^e(k).
%F Multiplicative with a(p^e) = A000045(A000720(p)+2)^e. - _David W. Wilson_, Aug 01 2001
%F Sum_{n>=1} 1/a(n) = 1 / A337669 = 5.269005... . - _Amiram Eldar_, Dec 24 2022
%t Table[Times @@ (Fibonacci[PrimePi[#[[1]]] + 2]^#[[2]] & /@ FactorInteger[n]), {n, 67}] (* _Ivan Neretin_, Aug 30 2015 *)
%o (PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k,1] = fibonacci(primepi(f[k, 1])+2)); factorback(f); \\ _Michel Marcus_, Jan 14 2021
%Y Cf. A000045, A000720, A051037, A337669.
%K nonn,mult
%O 1,2
%A _Marc LeBrun_, _N. J. A. Sloane_
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