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 A374205 #10 Dec 16 2024 08:46:23 %S A374205 0,0,0,1,0,0,0,0,1,0,1,0,0,2,0,0,0,0,1,0,0,0,0,2,0,0,1,0,1,0,1,0,0,2, %T A374205 0,0,0,2,2,0,0,0,2,1,0,0,0,0,3,2,0,0,1,3,0,0,0,0,1,0,0,0,0,1,0,0,0,0, %U A374205 1,0,0,0,0,2,2,0,0,0,1,0,0,0,0,1,0,1,0,0,1,2,1,0,0,3,0,0,0,0,2,0,0,0,1,1,0,0,0,0,1,2,0,0,0,2,0,0,0,2,1,0,0,1,2,3 %N A374205 The 5-adic valuation of A328845(n), where A328845 is a Fibonacci-based variant of the arithmetic derivative. %H A374205 Antti Karttunen, <a href="/A374205/b374205.txt">Table of n, a(n) for n = 2..100000</a> %F A374205 a(n) = A112765(A328845(n)). %t A374205 A374205[n_] := IntegerExponent[n*Total[MapApply[#2*Fibonacci[#]/# &, FactorInteger[n]]], 5]; %t A374205 Array[A374205, 100, 2] (* _Paolo Xausa_, Dec 16 2024 *) %o A374205 (PARI) %o A374205 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 A374205 A374205(n) = valuation(A328845(n), 5); %Y A374205 Cf. A000045, A112765, A328845. %Y A374205 Cf. also A374133, A374213, A374202. %K A374205 nonn %O A374205 2,14 %A A374205 _Antti Karttunen_, Jul 01 2024