A354870 - OEIS

%I #14 Dec 07 2023 21:37:51

%S 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,

%T 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,

%U 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

%N Number of nonprime squarefree divisors of n.

%C Number of terms of A000469 that divide n.

%H Antti Karttunen, <a href="/A354870/b354870.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

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

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

%F a(n) = A034444(n) - A001221(n). - _Ridouane Oudra_, Dec 07 2023

%p with(numtheory): seq(2^nops(factorset(n)) - nops(factorset(n)), n=1..80); # _Ridouane Oudra_, Dec 07 2023

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

%o (PARI)

%o A354819(n) = ((1!=bigomega(n))&&issquarefree(n));

%o A354870(n) = sumdiv(n,d,A354819(d));

%Y Inverse Möbius transform of A354819.

%Y Cf. A000469, A046523.

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

%Y Cf. A034444, A001221.

%K nonn

%O 1,6

%A _Antti Karttunen_, Jun 11 2022