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 A374203 #13 Dec 16 2024 05:12:48 %S A374203 0,0,0,0,0,0,1,1,1,0,0,0,1,0,0,0,1,0,0,0,3,0,0,0,0,3,0,0,0,0,0,0,0,0, %T A374203 1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,3,0,0,0,1,0,0,0,1,1,1,1,0,0,1,0, %U A374203 0,0,1,0,0,0,1,0,0,0,1,3,0,0,0,1,0,0,0,0,1,2,1,0,0,1,0,0,0,1,1,0,0,0,0,0,2,0,4 %N A374203 The 3-adic valuation of A328845(n), where A328845 is a Fibonacci-based variant of the arithmetic derivative. %H A374203 Antti Karttunen, <a href="/A374203/b374203.txt">Table of n, a(n) for n = 2..100000</a> %F A374203 a(n) = A007949(A328845(n)). %t A374203 A374203[n_] := IntegerExponent[n*Total[MapApply[#2*Fibonacci[#]/# &, FactorInteger[n]]], 3]; %t A374203 Array[A374203, 100, 2] (* _Paolo Xausa_, Dec 16 2024 *) %o A374203 (PARI) %o A374203 A328845(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*fibonacci(f[i,1])/f[i, 1])); %o A374203 A374203(n) = valuation(A328845(n), 3); %Y A374203 Cf. A007949, A328845, A374121, A374122 (after its 2 initial terms, gives the indices of nonzero terms in this sequence). %Y A374203 Cf. also A374133, A374213, A374202, A374205. %K A374203 nonn %O A374203 2,21 %A A374203 _Antti Karttunen_, Jul 01 2024