A353361 Number of divisors d of n for which A156552(d) is not a multiple of 3.

0, 1, 1, 1, 1, 3, 1, 2, 1, 2, 1, 4, 1, 3, 3, 2, 1, 4, 1, 3, 2, 2, 1, 6, 1, 3, 2, 4, 1, 5, 1, 3, 3, 2, 3, 5, 1, 3, 2, 4, 1, 6, 1, 3, 4, 2, 1, 7, 1, 3, 3, 4, 1, 6, 2, 6, 2, 3, 1, 8, 1, 2, 3, 3, 3, 5, 1, 3, 3, 6, 1, 8, 1, 3, 4, 4, 3, 6, 1, 5, 2, 2, 1, 8, 2, 3, 2, 4, 1, 7, 2, 3, 3, 2, 3, 9, 1, 4, 4, 4, 1, 5, 1, 6, 5

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

Cf. A000005, A003961, A156552, A348717, A353269, A353350, A353362.

Cf. also A353351.

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));
A353361(n) = sumdiv(n,d,!A353269(d));

Formula

a(n) = Sum_{d|n} (1-A353269(d)).

a(n) = A000005(n) - A353362(n).

a(p) = 1 for all primes p.

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