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A348968 a(n) = gcd(n, A099377(n)), where A099377(n) is the numerator of the harmonic mean of the divisors of n.

%I A348968 #9 Nov 09 2021 18:39:56
%S A348968 1,2,3,4,5,2,7,8,9,10,11,6,13,7,5,16,17,18,19,20,21,22,23,8,25,26,27,
%T A348968 1,29,10,31,32,11,34,35,36,37,38,39,8,41,7,43,22,45,23,47,24,49,50,17,
%U A348968 52,53,18,55,56,57,58,59,30,61,31,63,64,65,11,67,68,23,35,71,72,73,74,75,38,77,26,79,80,81,82,83,3
%N A348968 a(n) = gcd(n, A099377(n)), where A099377(n) is the numerator of the harmonic mean of the divisors of n.
%F A348968 a(n) = gcd(n, A099377(n)) = gcd(n, A348510(n)) = gcd(A099377(n), A348510(n)).
%F A348968 a(n) = n / A348969(n).
%F A348968 a(n) = A099377(n) / A057021(n). [Apparently, holds at least up to n = 2^25]
%o A348968 (PARI)
%o A348968 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A348968 A099377(n) = { my(d=divisors(n)); numerator(#d/sum(k=1, #d, 1/d[k])); }; \\ From A099377
%o A348968 A348968(n) = gcd(n, A099377(n));
%Y A348968 Cf. A057021, A099377, A348510, A348969.
%K A348968 nonn
%O A348968 1,2
%A A348968 _Antti Karttunen_, Nov 05 2021