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A330691 a(n) = gcd(n, A309639(n)), where A309639(n) is the index of the least harmonic number H_i whose denominator (A002805) is divisible by n.

%I A330691 #11 Jan 11 2022 08:29:32
%S A330691 1,2,3,4,5,3,7,8,9,5,11,4,13,7,5,16,17,9,19,5,3,11,23,3,25,13,27,7,29,
%T A330691 5,31,32,11,17,7,9,37,19,13,8,41,3,43,11,9,23,47,16,49,25,17,13,53,27,
%U A330691 11,8,19,29,59,5,61,31,9,64,13,11,67,17,3,7,71,9,73,37,25,19,11,13,79,16,81,41,83,3,17,43,29,11,89,9
%N A330691 a(n) = gcd(n, A309639(n)), where A309639(n) is the index of the least harmonic number H_i whose denominator (A002805) is divisible by n.
%H A330691 Antti Karttunen, <a href="/A330691/b330691.txt">Table of n, a(n) for n = 1..65537</a>
%F A330691 a(n) = gcd(n, A309639(n)).
%F A330691 a(n) = n/A330692(n).
%t A330691 A309639[n_] := For[k = 1, True, k++, If[Divisible[Denominator[ HarmonicNumber[k]], n], Return[k]]];
%t A330691 a[n_] := GCD[n, A309639[n]];
%t A330691 Array[a, 105]
%o A330691 (PARI) A330691(n) = gcd(n, A309639(n));
%Y A330691 Cf. A000961 (fixed points).
%Y A330691 Cf. A002805, A309639, A330692, A330742.
%K A330691 nonn
%O A330691 1,2
%A A330691 _Antti Karttunen_, Dec 29 2019