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%I #18 Jun 14 2022 02:27:22
%S 1,2,3,3,4,5,6,5,7,6,6,9,10,8,9,12,9,13,14,10,15,9,16,12,12,19,15,14,
%T 21,12,22,15,15,18,24,17,25,18,27,21,18,18,20,30,15,31,24,20,21,18,34,
%U 24,18,36,37,26,25,24,21,40,41,42,20,27,33,30,27,45,28,30,32,36,30,33,49
%N Arithmetic means of the divisors of unitary arithmetic numbers (i.e., of those for which the arithmetic mean of the unitary divisors is an integer, A103826).
%C The unitary arithmetic numbers are in A103826.
%H Amiram Eldar, <a href="/A103827/b103827.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A034448(A103826(n))/A034444(A103826(n)). - _Amiram Eldar_, Jun 19 2019
%e a(8) = 5 because the eighth unitary arithmetic number is A103826(8) = 12, the unitary divisors of 12 are 1, 3, 4 and 12 and (1 + 3 + 4 + 12)/4 = 5.
%p with(numtheory):unitdiv:=proc(n) local A, k: A:={}: for k from 1 to tau(n) do if gcd(divisors(n)[k],n/divisors(n)[k])=1 then A:=A union {divisors(n)[k]} else A:=A fi od end:utau:=n->nops(unitdiv(n)):usigma:=n->add(unitdiv(n)[j],j=1..nops(unitdiv(n))): p:=proc(n) if type(usigma(n)/utau(n), integer)=true then usigma(n)/utau(n) else fi end:seq(p(n),n=1..109);
%t Select[Table[Mean[Select[Divisors[n],GCD[#,n/#]==1&]],{n,150}],IntegerQ] (* _Harvey P. Dale_, May 20 2012 *)
%t Select[Times @@ ((1 + Power @@@ FactorInteger[#])/2) & /@ Range[100], IntegerQ] (* _Amiram Eldar_, Jun 14 2022 *)
%Y Cf. A034444, A034448, A103826.
%K nonn
%O 1,2
%A _Emeric Deutsch_, Feb 17 2005
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