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A377518 The largest divisor of n that is a term in A207481.

%I A377518 #7 Oct 31 2024 01:11:29
%S A377518 1,2,3,4,5,6,7,4,9,10,11,12,13,14,15,4,17,18,19,20,21,22,23,12,25,26,
%T A377518 27,28,29,30,31,4,33,34,35,36,37,38,39,20,41,42,43,44,45,46,47,12,49,
%U A377518 50,51,52,53,54,55,28,57,58,59,60,61,62,63,4,65,66,67,68,69
%N A377518 The largest divisor of n that is a term in A207481.
%C A377518 The number of these divisors is A377519(n), and their sum is A377520(n).
%H A377518 Amiram Eldar, <a href="/A377518/b377518.txt">Table of n, a(n) for n = 1..10000</a>
%F A377518 Multiplicative with a(p^e) = p^min(p, e).
%F A377518 a(n) = n if and only if n is in A207481.
%F A377518 Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (p^((p+1)*s) - p^(p+1) - p^(p*s) + p^p)/p^((p+1)*s).
%F A377518 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (1 - 1/(p^p * (p+1))) = 0.908130438292447963703... .
%t A377518 f[p_, e_] := p^Min[p, e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A377518 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,1]^min(f[i,1], f[i,2]));}
%Y A377518 Cf. A207481, A368329, A377515, A377519, A377520.
%K A377518 nonn,easy,mult
%O A377518 1,2
%A A377518 _Amiram Eldar_, Oct 30 2024