A353362 Number of divisors d of n for which A156552(d) is a multiple of 3.

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

Offset: 1

Author

Antti Karttunen, Apr 15 2022

Keywords

• nonn

Links

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

Crossrefs

Inverse Möbius transform of A353269.

Cf. A000005, A003961, A156552, A348717, A353303, A353304, A353361.

Cf. also A353352.

Differs from A353332 for the first time at n=30, where a(30) = 3, while A353332(30) = 2.

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 };
A353269(n) = (!(A156552(n)%3));
A353362(n) = sumdiv(n,d,A353269(d));

Formula

a(n) = Sum_{d|n} A353269(d).

a(n) = A000005(n) - A353361(n).

a(p) = 1 for all primes p.

a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.