login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A354870
Number of nonprime squarefree divisors of n.
3
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.
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.
Differs from A259936 for the first time at n=210, where a(210) = 12, while A259936(210) = 15.
Sequence in context: A323437 A339887 A259936 * A050320 A333175 A294893
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 11 2022
STATUS
approved