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%I #12 Jun 03 2020 05:28:16
%S 1,2,3,6,14,15,30,35,42,44,60,70,78,105,126,132,190,210,220,312,357,
%T 418,558,570,660,693,714,728,910,1045,1254,1386,1395,1428,1540,2090,
%U 2108,2184,2730,2790,3135,3465,3640,3692,3762,4522,4620,4674,5236,5278,6270
%N Unitary balanced numbers: numbers k such that uphi(k) (A047994) divides usigma(k) (A034448).
%C Terms that are also balanced numbers (A020492) include the squarefree balanced numbers (A078557). The nonsquarefree common terms are in A335289.
%H Amiram Eldar, <a href="/A335288/b335288.txt">Table of n, a(n) for n = 1..10000</a>
%e 6 is a term since usigma(6) = 12 is divisible by uphi(6) = 2.
%t f[1, 1] = 1; f[p_, e_]:= (p^e + 1)/(p^e -1); ubalQ[n_] := IntegerQ[Times @@ (f @@@ FactorInteger[n])]; Select[Range[10^4], ubalQ]
%Y The unitary version of A020492.
%Y A078557 is a subsequence.
%Y Cf. A034448, A047994, A335289.
%K nonn
%O 1,2
%A _Amiram Eldar_, May 30 2020
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