A374203 - OEIS

%I #13 Dec 16 2024 05:12:48

%S 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 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 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 The 3-adic valuation of A328845(n), where A328845 is a Fibonacci-based variant of the arithmetic derivative.

%H Antti Karttunen, <a href="/A374203/b374203.txt">Table of n, a(n) for n = 2..100000</a>

%F a(n) = A007949(A328845(n)).

%t A374203[n_] := IntegerExponent[n*Total[MapApply[#2*Fibonacci[#]/# &, FactorInteger[n]]], 3];

%t Array[A374203, 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 A374203(n) = valuation(A328845(n), 3);

%Y Cf. A007949, A328845, A374121, A374122 (after its 2 initial terms, gives the indices of nonzero terms in this sequence).

%Y Cf. also A374133, A374213, A374202, A374205.

%K nonn

%O 2,21

%A _Antti Karttunen_, Jul 01 2024