A374133 The 3-adic valuation of A276085(n), where A276085 is the primorial base log-function.

0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 0, 0, 2, 1, 1, 0, 0, 2, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 3, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 2, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 2, 1, 2, 0, 0, 1, 0, 1

Offset: 2

Author

Antti Karttunen, Jun 30 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A007949, A276085, A339746 (indices of nonzero terms), A372573 (their characteristic function).

Cf. also A373153, A374132.

Programs

PARI

A276085(n) = { my(f=factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
A374133(n) = valuation(A276085(n),3);

Formula

a(n) = A007949(A276085(n)).