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The 5-adic valuation of A328845(n), where A328845 is a Fibonacci-based variant of the arithmetic derivative.
5

%I #6 Jul 01 2024 08:48:16

%S 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 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 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 The 5-adic valuation of A328845(n), where A328845 is a Fibonacci-based variant of the arithmetic derivative.

%H Antti Karttunen, <a href="/A374205/b374205.txt">Table of n, a(n) for n = 2..100000</a>

%F a(n) = A112765(A328845(n)).

%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 A374205(n) = valuation(A328845(n), 5);

%Y Cf. A000045, A112765, A328845.

%Y Cf. also A374133, A374213, A374202.

%K nonn

%O 2,14

%A _Antti Karttunen_, Jul 01 2024