A003965 Fully multiplicative with a(prime(k)) = Fibonacci(k+2).

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, 27, 32, 144, 30, 233, 32, 39, 68, 40, 36, 377, 110, 63, 40, 610, 48, 987, 52, 45, 178, 1597, 48, 64, 50, 102, 84, 2584, 54, 65, 64, 165, 288, 4181, 60, 6765, 466, 72, 64, 105, 78, 10946

Offset: 1

Author

Marc LeBrun, N. J. A. Sloane

Keywords

• nonn
• mult

Comments

Numbers k such that a(k) = k are exactly 5-smooth numbers (A051037). - Ivan Neretin, Aug 30 2015

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A000720, A051037, A337669.

Programs

Mathematica

Table[Times @@ (Fibonacci[PrimePi[#[[1]]] + 2]^#[[2]] & /@ FactorInteger[n]), {n, 67}] (* Ivan Neretin, Aug 30 2015 *)

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

Formula

If n = Product p(k)^e(k) then a(n) = Product Fibonacci(k+2)^e(k).

Multiplicative with a(p^e) = A000045(A000720(p)+2)^e. - David W. Wilson, Aug 01 2001

Sum_{n>=1} 1/a(n) = 1 / A337669 = 5.269005... . - Amiram Eldar, Dec 24 2022