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%I #9 Jul 22 2020 02:20:50
%S 1,6,45,60,90,270,420,630,2970,5460,8190,9100,15925,27300,36720,40950,
%T 46494,47520,54600,81900,95550,136500,163800,172900,204750,232470,
%U 245700,257040,332640,409500,464940,491400,646425,716625,790398,791700,819000,900900,929880
%N Tri-unitary harmonic numbers: numbers k such that the harmonic mean of the tri-unitary divisors of k is an integer.
%C Equivalently, numbers k such that A324706(k) | (k * A335385(k)).
%C Differs from A063947 from n >= 18.
%H Amiram Eldar, <a href="/A335387/b335387.txt">Table of n, a(n) for n = 1..200</a>
%e 45 is a term since its tri-unitary divisors are {1, 5, 9, 45} and their harmonic mean, 3, in an integer.
%t f1[p_, e_] := If[e == 3 || e == 6, 4, 2]; f2[p_, e_] := If[e == 3, (p^4 - 1)/(p - 1), If[e == 6, (p^8 - 1)/(p^2 - 1), p^e + 1]]; f[p_, e_] := p^e * f1[p, e]/f2[p, e]; tuhQ[1] = True; tuhQ[n_] := IntegerQ[Times @@ (f @@@ FactorInteger[n])]; Select[Range[10^4], tuhQ]
%Y A324707 is a subsequence.
%Y Analogous sequences: A001599 (harmonic numbers), A006086 (unitary), A063947 (infinitary), A286325 (bi-unitary), A319745 (nonunitary).
%Y Cf. A324706, A335385.
%K nonn
%O 1,2
%A _Amiram Eldar_, Jun 04 2020
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