A374202 - OEIS

%I #12 Dec 16 2024 05:12:39

%S 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 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 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 The 2-adic valuation of A328845(n), where A328845 is a Fibonacci-based variant of the arithmetic derivative.

%H Antti Karttunen, <a href="/A374202/b374202.txt">Table of n, a(n) for n = 2..100000</a>

%F a(n) = A007814(A328845(n)).

%t A374202[n_] := IntegerExponent[n*Total[MapApply[#2*Fibonacci[#]/# &, FactorInteger[n]]], 2];

%t Array[A374202, 100, 2] (* _Paolo Xausa_, Dec 16 2024 *)

%o (PARI)

%o 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(n) = valuation(A328845(n), 2);

%Y 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 Cf. also A374132, A374212, A374203, A374205.

%K nonn,changed

%O 2,3

%A _Antti Karttunen_, Jul 01 2024