A353364 Inverse Möbius transform of A332814.

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

Offset: 1

Author

Antti Karttunen, Apr 15 2022

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A003961, A156552, A332814.

Cf. also A353354, A353361, A353362.

Programs

PARI

A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A332814(n) = { my(u=A156552(n)%3); if(2==u,-1,u); };
A353364(n) = sumdiv(n,d,A332814(d));

Formula

a(n) = Sum_{d|n} A332814(d).

For all n >= 1, a(A003961(n)) = -a(n), a(A000040(n)) = ((-1)^(n-1)).