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%I #19 Mar 30 2024 18:48:22
%S 1,1,2,1,5,2,13,1,4,5,89,2,233,13,10,1,1597,4,4181,5,26,89,28657,2,25,
%T 233,8,13,514229,10,1346269,1,178,1597,65,4,24157817,4181,466,5,
%U 165580141,26,433494437,89,20,28657,2971215073,2,169,25,3194,233
%N Replace each prime p in prime-factorization of n with p-th Fibonacci number.
%C If, for p = prime, p^(m_{n,p}) is highest power of p dividing n, m = nonnegative integer, then a(n) is product over all primes of F(p)^(m_{n,p}), where F(p) = p-th Fibonacci number (A000045).
%H Danny Rorabaugh, <a href="/A113175/b113175.txt">Table of n, a(n) for n = 1..4000</a>
%F Totally multiplicative with a(p) = F(p). - _Franklin T. Adams-Watters_, Jun 05 2006
%e 63 = 3^2 * 7^1. So a(63) = F(3)^2 * F(7)^1 = 4 * 13 = 52.
%t Times@@@Table[Fibonacci[#[[1]]]^#[[2]]&/@FactorInteger[n],{n,60}] (* _Harvey P. Dale_, Mar 30 2024 *)
%o (Sage) [1]+[prod([fibonacci(x[0])^x[1] for x in factor(n)]) for n in range(2,53)] # _Danny Rorabaugh_, Apr 03 2015
%Y Cf. A113176, A000045.
%K mult,nonn,easy
%O 1,3
%A _Leroy Quet_, Oct 16 2005
%E More terms from Esa Peuha (esa.peuha(AT)helsinki.fi), Oct 26 2005
%E Previous Mathematica program deleted by _Harvey P. Dale_, Mar 30 2024
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