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

2,3

Links

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

Formula

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

Prog

(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);

Crossrefs

Cf. A007814, A328768.

Cf. also A374132, A374213.

Sequence in context: A378716 A362421 A323302 * A303903 A348515 A209318

Adjacent sequences: A374209 A374210 A374211 * A374213 A374214 A374215

Keyword

nonn

Author

Antti Karttunen, Jun 30 2024

Status

approved