This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A351219 #19 Jan 05 2025 19:51:42
%S A351219 1,1,1,2,1,1,1,3,2,1,1,2,1,1,1,5,1,2,1,2,1,1,1,3,2,1,3,2,1,1,1,8,1,1,
%T A351219 1,4,1,1,1,3,1,1,1,2,2,1,1,5,2,2,1,2,1,3,1,3,1,1,1,2,1,1,2,13,1,1,1,2,
%U A351219 1,1,1,6,1,1,2,2,1,1,1,5,5,1,1,2,1,1,1
%N A351219 Multiplicative with a(p^e) = Fibonacci(e+1).
%C A351219 These numbers were called Zetanacci numbers by Bruckman (1983).
%C A351219 The distinct values of the terms are in A065108.
%H A351219 Amiram Eldar, <a href="/A351219/b351219.txt">Table of n, a(n) for n = 1..10000</a>
%H A351219 Paul S. Bruckman, <a href="https://fq.math.ca/Scanned/21-3/advanced21-3.pdf">Problem H-359</a>, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 21, No. 3 (1983), p. 238; <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/23-1/advanced23-1.pdf">Zetanacci</a>, Solution to Problem H-359 by C. Georghiou, ibid., Vol. 23, No. 1 (1985), pp. 91-92.
%F A351219 Dirichlet g.f.: Product_{p prime} 1/(1 - p^(-s) - p^(-2*s)).
%F A351219 a(n) = 1 if and only if n is a squarefree number (A005117).
%F A351219 Sum_{k=1..n} a(k) ~ c * n, where c = A065488 = Product_{p primes} (1 + 1/(p^2 - p - 1)) = 2.67411272557... - _Vaclav Kotesovec_, Feb 10 2022
%t A351219 f[p_, e_] := Fibonacci[e + 1]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A351219 (PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k,1] = fibonacci(f[k,2]+1); f[k,2]=1); factorback(f); \\ _Michel Marcus_, Feb 05 2022
%o A351219 (Python)
%o A351219 from math import prod
%o A351219 from sympy import factorint, fibonacci
%o A351219 def a(n): return prod(fibonacci(e+1) for p, e in factorint(n).items())
%o A351219 print([a(n) for n in range(1, 88)]) # _Michael S. Branicky_, Feb 05 2022
%o A351219 (PARI) for(n=1, 100, print1(direuler(p=2, n, 1/(1 - X - X^2))[n], ", ")) \\ _Vaclav Kotesovec_, Feb 10 2022
%Y A351219 Cf. A000045, A005117, A065108, A065488.
%K A351219 nonn,mult,easy
%O A351219 1,4
%A A351219 _Amiram Eldar_, Feb 05 2022