A374213 - OEIS

%I #8 Jun 30 2024 22:13:14

%S 0,0,0,1,0,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,1,0,1,0,3,0,1,0,1,0,0,0,1,

%T 1,1,0,0,3,1,0,1,0,1,0,1,0,1,0,0,0,1,3,2,4,0,0,1,0,1,0,1,1,2,0,1,0,0,

%U 0,1,1,1,0,0,0,2,0,1,0,3,0,1,0,1,0,0,1,1,1,2,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,4

%N The 3-adic valuation of A328768(n), where A328768 is the first primorial based variant of the arithmetic derivative.

%H Antti Karttunen, <a href="/A374213/b374213.txt">Table of n, a(n) for n = 2..100000</a>

%F a(n) = A007949(A328768(n)).

%o (PARI)

%o A002110(n) = prod(i=1,n,prime(i));

%o A328768(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i,1])-1)/f[i, 1]));

%o A374213(n) = valuation(A328768(n), 3);

%Y Cf. A007949, A328768, A373991, A373992 (after its two initial terms, gives the indices of nonzero terms in this sequence).

%Y Cf. also A374133, A374212.

%K nonn

%O 2,26

%A _Antti Karttunen_, Jun 30 2024