A353332 Number of divisors d of n for which both A001222(d) and A056239(d) are even.

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

Offset

1,4

Comments

Number of terms of A340784 that divide n.

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} A353331(d).

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

Example

Of the 9 divisors of 36, only divisors 1, 4, 9 and 36 satisfy the condition, therefore a(36) = 4.

Prog

(PARI)
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1]))); }
A353331(n) = ((!(bigomega(n)%2)) && (!(A056239(n)%2)));
A353332(n) = sumdiv(n, d, A353331(d));

Crossrefs

Cf. A001222, A003961, A056239, A340784, A348717.

Inverse Möbius transform of A353331. Cf. also A353333, A353334.

Differs from A353362 for the first time at n=30, where a(30) = 2, while A353362(30) = 3.

Sequence in context: A079487 A229122 A069010 * A353362 A256122 A087048

Adjacent sequences: A353329 A353330 A353331 * A353333 A353334 A353335

Keyword

nonn

Author

Antti Karttunen, Apr 14 2022

Status

approved