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A365635 The largest divisor of n that is a term of A048102.

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%I A365635 #20 Sep 20 2023 01:44:30
%S A365635 1,1,1,4,1,1,1,4,1,1,1,4,1,1,1,4,1,1,1,4,1,1,1,4,1,1,27,4,1,1,1,4,1,1,
%T A365635 1,4,1,1,1,4,1,1,1,4,1,1,1,4,1,1,1,4,1,27,1,4,1,1,1,4,1,1,1,4,1,1,1,4,
%U A365635 1,1,1,4,1,1,1,4,1,1,1,4,27,1,1,4,1,1
%N A365635 The largest divisor of n that is a term of A048102.
%H A365635 Amiram Eldar, <a href="/A365635/b365635.txt">Table of n, a(n) for n = 1..10000</a>
%H A365635 Vaclav Kotesovec, <a href="/A365635/a365635.pdf">Graphs - the asymptotic ratio (10^7, 10^8 and 10^9 terms)</a>.
%F A365635 Multiplicative with a(p^e) = 1 if e < p and p^p otherwise.
%F A365635 a(n) <= n with equality if and only if n is in A048102.
%F A365635 a(n) >= 1 with equality if and only if n is in A048103.
%F A365635 Dirichlet g.f.: zeta(s) * Product_{p prime} (1 + (p^p-1)/p^(p*s)).
%t A365635 f[p_, e_] := p^If[e < p, 0, p]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A365635 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i,2] < f[i,1], 1, f[i, 1]^f[i,1]));}
%Y A365635 Cf. A048102, A048103, A327939, A365634.
%K A365635 nonn,easy,mult
%O A365635 1,4
%A A365635 _Amiram Eldar_, Sep 14 2023