A374213 The 3-adic valuation of A328768(n), where A328768 is the first primorial based variant of the arithmetic derivative.

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, 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, 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

Offset

2,26

Links

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

Formula

a(n) = A007949(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]));
A374213(n) = valuation(A328768(n), 3);

Crossrefs

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

Cf. also A374133, A374212.

Sequence in context: A317946 A347439 A347048 * A140807 A232629 A340007

Adjacent sequences: A374210 A374211 A374212 * A374214 A374215 A374216

Keyword

nonn

Author

Antti Karttunen, Jun 30 2024

Status

approved