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

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from indices in prime factorization

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.

Prog

(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));

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.

Sequence in context: A229122 A069010 A353332 * A256122 A087048 A109700

Adjacent sequences: A353359 A353360 A353361 * A353363 A353364 A353365

Keyword

nonn

Author

Antti Karttunen, Apr 15 2022

Status

approved