%I #7 Oct 06 2023 10:56:15
%S 1,2,3,1,5,6,7,2,1,10,11,3,13,14,15,16,17,2,19,5,21,22,23,6,1,26,3,7,
%T 29,30,31,32,33,34,35,1,37,38,39,10,41,42,43,11,5,46,47,48,1,2,51,13,
%U 53,6,55,14,57,58,59,15,61,62,7,16,65,66,67,17,69,70,71
%N The largest infinitary divisor of n that is a term of A366242.
%H Amiram Eldar, <a href="/A366244/b366244.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = p^A063694(e).
%F a(n) = n / A366245(n).
%F a(n) >= 1, with equality if and only if n is a term of A366243.
%F a(n) <= n, with equality if and only if n is a term of A366242.
%F Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Product_{p prime} (1-1/p)*(Sum_{k>=1} p^(A063694(k)-2*k)) = 0.35319488024808595542... .
%t f[p_, e_] := p^BitAnd[e, Sum[2^k, {k, 0, Floor@ Log2[e], 2}]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o (PARI) s(e) = sum(k = 0, e, (-2)^k*floor(e/2^k));
%o a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,1]^s(f[i,2]));}
%Y Cf. A063694, A366242, A366243, A366245.
%K nonn,easy,mult
%O 1,2
%A _Amiram Eldar_, Oct 05 2023