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

1,6

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

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

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 *)

Prog

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

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.

Sequence in context: A323437 A339887 A259936 * A050320 A333175 A294893

Adjacent sequences: A354867 A354868 A354869 * A354871 A354872 A354873

Keyword

nonn

Author

Antti Karttunen, Jun 11 2022

Status

approved