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%I #7 Dec 07 2023 10:24:51
%S 1,1,1,3,1,1,1,1,4,1,1,3,1,1,1,3,1,4,1,3,1,1,1,1,6,1,1,3,1,1,1,1,1,1,
%T 1,12,1,1,1,1,1,1,1,3,4,1,1,3,8,6,1,3,1,1,1,1,1,1,1,3,1,1,4,3,1,1,1,3,
%U 1,1,1,4,1,1,6,3,1,1,1,3,4,1,1,3,1,1,1
%N Sum of the squarefree divisors of the largest unitary divisor of n that is a square.
%H Amiram Eldar, <a href="/A367990/b367990.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = p + 1 if e is even and 1 otherwise.
%F a(n) = A048250(A350388(n)).
%F a(n) = A000203(A336643(n)).
%F a(n) = A048250(n)/A367991(n).
%F a(n) >= 1, with equality if and only if n is an exponentially odd number (A268335).
%F Dirichlet g.f.: zeta(2*s) * Product_{p prime} (1 + 1/p^s + 1/p^(2*s-1)).
%t f[p_, e_] := If[EvenQ[e], p + 1, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(!(f[i,2]%2), f[i,1]+1, 1));}
%Y Cf. A000203, A048250, A268335, A336643, A350388, A367991.
%K nonn,easy,mult
%O 1,4
%A _Amiram Eldar_, Dec 07 2023
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