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A348509 a(n) is the numerator of the harmonic mean of the divisors of A003961(n).

%I A348509 #11 Nov 01 2021 19:21:00
%S A348509 1,3,5,27,7,5,11,27,75,21,13,45,17,11,35,405,19,225,23,189,55,39,29,9,
%T A348509 49,17,125,99,31,35,37,729,65,57,77,2025,41,23,85,189,43,55,47,27,525,
%U A348509 29,53,675,363,147,19,51,59,125,13,99,115,93,61,315,67,111,275,5103,119,65,71,513,29,77,73,405,79,41,245
%N A348509 a(n) is the numerator of the harmonic mean of the divisors of A003961(n).
%H A348509 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A348509 a(n) = A099377(A003961(n)).
%F A348509 a(n) = A336845(n) / A336846(n).
%t A348509 f[p_, e_] := (e + 1)*(pn = NextPrime[p])^e*(pn - 1)/(pn^(e + 1) - 1); a[1] = 1; a[n_] := Numerator[Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* _Amiram Eldar_, Oct 31 2021 *)
%o A348509 (PARI)
%o A348509 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A348509 A099377(n) = { my(d=divisors(n)); numerator(#d/sum(k=1, #d, 1/d[k])); }; \\  From A099377
%o A348509 A348509(n) = A099377(A003961(n));
%Y A348509 Cf. A003961, A099377, A336845, A336846.
%Y A348509 Cf. A336848 (denominators).
%K A348509 nonn,frac
%O A348509 1,2
%A A348509 _Antti Karttunen_, Oct 31 2021