A354870 Number of nonprime squarefree divisors of n.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 5, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 5, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 5, 1, 2, 2, 1, 2, 5, 1, 2, 2, 5, 1, 2, 1, 2, 2, 2, 2, 5, 1, 2, 1, 2, 1, 5, 2, 2, 2, 2, 1, 5, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 5, 1, 2, 5

Offset: 1

Author

Antti Karttunen, Jun 11 2022

Keywords

• nonn

Comments

Number of terms of A000469 that divide n.

Links

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

Crossrefs

Inverse Möbius transform of A354819.

Cf. A000469, A046523.

Differs from A259936 for the first time at n=210, where a(210) = 12, while A259936(210) = 15.

Cf. A034444, A001221.

Programs

Maple

with(numtheory): seq(2^nops(factorset(n)) - nops(factorset(n)), n=1..80); # Ridouane Oudra, Dec 07 2023

Mathematica

a[n_] := DivisorSum[n, 1 &, ! PrimeQ[#] && SquareFreeQ[#] &]; Array[a, 100] (* Amiram Eldar, Jun 11 2022 *)

PARI

A354819(n) = ((1!=bigomega(n))&&issquarefree(n));
A354870(n) = sumdiv(n,d,A354819(d));

Formula

a(n) = Sum_{d|n} A354819(d).

For all n >= 1, a(n) = a(A046523(n)).

a(n) = A034444(n) - A001221(n). - Ridouane Oudra, Dec 07 2023