cp's OEIS Frontend

A368885 The number of unitary divisors of n that are squares of a squarefree number (A062503).

%I A368885 #13 Jan 10 2024 00:29:42
%S A368885 1,1,1,2,1,1,1,1,2,1,1,2,1,1,1,1,1,2,1,2,1,1,1,1,2,1,1,2,1,1,1,1,1,1,
%T A368885 1,4,1,1,1,1,1,1,1,2,2,1,1,1,2,2,1,2,1,1,1,1,1,1,1,2,1,1,2,1,1,1,1,2,
%U A368885 1,1,1,2,1,1,2,2,1,1,1,1,1,1,1,2,1,1,1
%N A368885 The number of unitary divisors of n that are squares of a squarefree number (A062503).
%C A368885 First differs from A294932 at n = 32.
%C A368885 The largest of these divisors is A368884(n).
%H A368885 Amiram Eldar, <a href="/A368885/b368885.txt">Table of n, a(n) for n = 1..10000</a>
%F A368885 Multiplicative with a(p^e) = 2 if e = 2, and 1 otherwise.
%F A368885 a(n) >= 1, with equality if and only if n is in A337050.
%F A368885 a(n) <= A034444(n), with equality if and only if n is in A062503.
%F A368885 Dirichlet g.f.: zeta(s) * Product_{p prime} (1 + 1/p^(2*s) - 1/p^(3*s)).
%F A368885 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + 1/p^2 - 1/p^3) = 1.30596827416754083231... .
%t A368885 f[p_, e_] := If[e == 2, 2, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A368885 (PARI) a(n) = vecprod(apply(x->if(x==2, 2, 1), factor(n)[, 2]));
%o A368885 (Python)
%o A368885 from sympy import factorint
%o A368885 def A368885(n): return 1<<sum(1 for e in factorint(n).values() if e==2) # _Chai Wah Wu_, Jan 09 2024
%Y A368885 Cf. A034444, A062503, A294932, A337050, A368884.
%K A368885 nonn,easy,mult
%O A368885 1,4
%A A368885 _Amiram Eldar_, Jan 09 2024