A374132 The 2-adic valuation of A276085(n), where A276085 is the primorial base log-function.

0, 1, 1, 1, 0, 1, 0, 2, 0, 1, 2, 1, 0, 3, 2, 1, 0, 1, 3, 5, 0, 1, 0, 2, 0, 1, 5, 1, 0, 1, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 0, 1, 2, 1, 0, 1, 1, 2, 0, 4, 3, 1, 0, 3, 0, 4, 0, 1, 1, 1, 0, 1, 1, 2, 0, 1, 4, 2, 0, 1, 0, 1, 0, 1, 4, 4, 0, 1, 1, 3, 0, 1, 1, 2, 0, 3, 0, 1, 0, 2, 2, 4, 0, 2, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 3

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, A276085.

Cf. A036554 (indices of 0's), A003159 (of nonzero terms), A373142 (of 1's), A373267 (of 2's), A369002 (of terms >= 2), A373138 (of terms >= 3).

Cf. also A374133.

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))); };
A374132(n) = valuation(A276085(n),2);

Formula

a(n) = A007814(A276085(n)).