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 A113177 #23 Jul 08 2024 13:59:23
%S A113177 0,1,2,2,5,3,13,3,4,6,89,4,233,14,7,4,1597,5,4181,7,15,90,28657,5,10,
%T A113177 234,6,15,514229,8,1346269,5,91,1598,18,6,24157817,4182,235,8,
%U A113177 165580141,16,433494437,91,9,28658,2971215073,6,26,11,1599,235,53316291173,7,94
%N A113177 Fully additive with a(p) = Fibonacci(p); If, for p prime, p^(m_{n,p}) is the highest power of p dividing n with m>=0, then a(n) = Sum_{p prime} F(p)*(m_{n,p}), where F(p) = p-th Fibonacci number.
%H A113177 Danny Rorabaugh, <a href="/A113177/b113177.txt">Table of n, a(n) for n = 1..4000</a>
%F A113177 Totally additive with a(p) = A000045(p).
%e A113177 12 = 2^2 * 3^1, so a(12) = F(2)*2 + F(3)*1 = 2 + 2 = 4.
%t A113177 b[t_]:=Fibonacci[First[t]]Last[t] a[n_]:=Apply[Plus, Map[b, FactorInteger[n]]] (* Esa Peuha, Oct 26 2005 *)
%o A113177 (PARI) { for(n=1,100,f=factor(n);s=0;for(i=1,matsize(f)[1],s+=fibonacci(f[i,1])*f[i,2]);print1(s,",")) } \\ Lambert Klasen, Oct 26 2005
%o A113177 (Sage) [0]+[sum([fibonacci(x[0])*x[1] for x in factor(n)]) for n in range(2,56)] # _Danny Rorabaugh_, Apr 03 2015
%Y A113177 Cf. A000045, A113178.
%Y A113177 Cf. A373586 (indices of even terms), A373587 (of odd terms), A374052 (of multiples of 3), A374206 (2-adic valuation), A374207 (3-adic valuation), A374208 (5-adic valuation), A374209 [A007895(a(n))], A374124 [a(n) mod 360].
%Y A113177 Cf. A374106 [gcd(a(n), A328845(n))], A374112 [gcd(a(n), A276085(n))].
%Y A113177 For other completely additive sequences see the cross-references in A001414.
%K A113177 nonn,easy
%O A113177 1,3
%A A113177 _Leroy Quet_, Oct 16 2005
%E A113177 More terms from Esa Peuha (esa.peuha(AT)helsinki.fi) and Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 26 2005
%E A113177 Prefixed the name with a more succinct form of the definition given in comments. - _Antti Karttunen_, Jul 08 2024