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 A374202 #12 Dec 16 2024 05:12:39 %S A374202 0,1,2,0,0,0,2,2,0,0,2,0,0,0,5,0,0,0,3,0,0,0,2,1,0,1,4,0,0,0,4,0,0,2, %T A374202 2,0,0,0,2,0,0,0,4,0,0,0,7,1,0,0,3,0,0,2,2,0,0,0,5,0,0,0,6,1,0,0,3,0, %U A374202 0,0,2,0,0,3,5,1,0,0,4,3,0,0,3,1,0,0,2,0,0,3,5,0,0,3,4,0,0,0,2,0,0,0,2,1,0,0,2 %N A374202 The 2-adic valuation of A328845(n), where A328845 is a Fibonacci-based variant of the arithmetic derivative. %H A374202 Antti Karttunen, <a href="/A374202/b374202.txt">Table of n, a(n) for n = 2..100000</a> %F A374202 a(n) = A007814(A328845(n)). %t A374202 A374202[n_] := IntegerExponent[n*Total[MapApply[#2*Fibonacci[#]/# &, FactorInteger[n]]], 2]; %t A374202 Array[A374202, 100, 2] (* _Paolo Xausa_, Dec 16 2024 *) %o A374202 (PARI) %o A374202 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 A374202 A374202(n) = valuation(A328845(n), 2); %Y A374202 Cf. A007814, A328845, A374045, A374046 (after its 2 initial terms, gives the indices of nonzero terms in this sequence), A374047 (indices of 0's). %Y A374202 Cf. also A374132, A374212, A374203, A374205. %K A374202 nonn %O A374202 2,3 %A A374202 _Antti Karttunen_, Jul 01 2024