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

1,15

Links

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

Formula

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

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Inverse Möbius transform of A353558.

Cf. A001227, A067019, A369257.

Sequence in context: A368774 A005087 A050332 * A337930 A340691 A216658

Adjacent sequences: A369255 A369256 A369257 * A369259 A369260 A369261

Keyword

nonn

Author

Antti Karttunen, Jan 24 2024

Status

approved