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Nonprimes q such that antiharmonic mean B(q) of the numbers k < q such that gcd(k, q) = 1 is integer, where B(q) = A053818(q) / A023896(q) = A175505(q) / A175506(q).
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%I #14 Aug 02 2019 21:31:54

%S 1,10,22,34,46,55,58,82,85,91,94,106,110,115,118,133,142,145,166,170,

%T 178,182,187,202,205,214,217,226,230,235,247,253,259,262,265,266,274,

%U 290,295,298,301,319,334,346,355,358,374,382,391,394,403,410,415,427

%N Nonprimes q such that antiharmonic mean B(q) of the numbers k < q such that gcd(k, q) = 1 is integer, where B(q) = A053818(q) / A023896(q) = A175505(q) / A175506(q).

%C Nonprimes q such that A175506(q) = 1. Subsequence of A179871. Union a(n) and A003627 = A179871. Corresponding values of B(q) in A179890.

%H G. C. Greubel, <a href="/A179887/b179887.txt">Table of n, a(n) for n = 1..1653</a>

%e a(6) = 55 because B(55) = A053818(55) / A023896(55) = 40700 / 1100 = 37 (integer).

%t f[n_] := 2 Plus @@ (Select[ Range@n, GCD[ #, n] == 1 &]^2)/(n*EulerPhi@n); Select[ Range@ 433, ! PrimeQ@# && IntegerQ@ f@# &] (* _Robert G. Wilson v_, Aug 02 2010 *)

%Y Cf. A179871, A179872, A179873, A179874, A179875, A179876, A179877, A179878, A179879, A179880, A179882, A179883, A179884, A179885, A179887, A179890, A179891.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Jul 30 2010, Jul 31 2010

%E More terms from _Robert G. Wilson v_, Aug 02 2010