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

Author

Antti Karttunen, Apr 14 2022

Keywords

• nonn

Comments

Number of terms of A340784 that divide n.

Examples

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

Links

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

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.

Programs

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));

Formula

a(n) = Sum_{d|n} A353331(d).

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