A369258 a(n) = number of odd divisors of n that have an odd number of prime factors with multiplicity.

0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 0, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 3, 0, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 3, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 3, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 2, 1, 1, 4

Offset: 1

Author

Antti Karttunen, Jan 24 2024

Keywords

• nonn

Examples

			Of the eight odd divisors of 105, the four divisors 3, 5, 7, 105 all have an odd number of prime factors (A001222(d) is odd), therefore a(105) = 4.
		

Links

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

Crossrefs

Inverse Möbius transform of A353558.

Cf. A001227, A067019, A369257.

Programs

Mathematica

Array[DivisorSum[#, 1 &, And[OddQ[#], OddQ@ PrimeOmega[#]] &] &, 120] (* Michael De Vlieger, Jan 24 2024 *)

PARI

A353558(n) = ((n%2)&&(bigomega(n)%2));
A369258(n) = sumdiv(n,d,A353558(d));

Formula

a(n) = Sum_{d|n} A353558(d).

a(n) = A001227(n) - A369257(n).