A374212 The 2-adic valuation of A328768(n), where A328768 is the first primorial based variant of the arithmetic derivative.

0, 1, 2, 1, 0, 1, 2, 2, 0, 1, 2, 1, 0, 2, 5, 1, 0, 1, 2, 3, 0, 1, 2, 2, 0, 1, 2, 1, 0, 1, 4, 2, 0, 6, 2, 1, 0, 2, 2, 1, 0, 1, 2, 1, 0, 1, 7, 2, 0, 2, 2, 1, 0, 2, 2, 4, 0, 1, 2, 1, 0, 1, 6, 2, 0, 1, 2, 2, 0, 1, 2, 1, 0, 1, 2, 3, 0, 1, 8, 3, 0, 1, 2, 2, 0, 2, 2, 1, 0, 4, 2, 3, 0, 3, 4, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2

Offset: 2

Author

Antti Karttunen, Jun 30 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 2..100000

Crossrefs

Cf. A007814, A328768.

Cf. also A374132, A374213.

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
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]));
A374212(n) = valuation(A328768(n), 2);

Formula

a(n) = A007814(A328768(n)).