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%I #6 Dec 21 2023 21:15:22
%S 1,1,1,1,1,1,1,4,1,1,1,1,1,1,1,5,1,1,1,1,1,1,1,4,1,1,1,1,1,1,1,6,1,1,
%T 1,1,1,1,1,4,1,1,1,1,1,1,1,5,1,1,1,1,1,1,1,4,1,1,1,1,1,1,1,7,1,1,1,1,
%U 1,1,1,4,1,1,1,1,1,1,1,5,5,1,1,1,1,1,1
%N The number of divisors of the largest term of A054743 that divides of n.
%C First differs from A366145 at n = 27.
%H Amiram Eldar, <a href="/A368331/b368331.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = 1 if e <= p, and a(p^e) = e+1 if e > p.
%F a(n) = A000005(A368329(n)).
%F a(n) >= 1, with equality if and only if n is in A207481.
%F a(n) <= A000005(n), with equality if and only if n is in A054743.
%F Dirichlet g.f.: zeta(s)^2 * Product_{p prime} (1 - 1/p^s - 1/p^((p+2)*s-1) + 1/p^((p+1)*s) + 1/p^((p+1)*s-1)).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + 1/((p-1)*p^(p-1))) = 1.58396891058853238595... .
%t f[p_, e_] := If[e <= p, 1, e+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] <= f[i,1], 1, f[i,2]+1));}
%Y Cf. A000005, A054743, A207481, A368328, A368329, A368330, A368335, A368336.
%Y Cf. A366145.
%K nonn,easy,mult
%O 1,8
%A _Amiram Eldar_, Dec 21 2023
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