A179871 - OEIS

%I #9 Aug 02 2019 21:58:07

%S 1,2,5,10,11,17,22,23,29,34,41,46,47,53,55,58,59,71,82,83,85,89,91,94,

%T 101,106,107,110,113,115,118,131,133,137,142,145,149,166,167,170,173,

%U 178,179,182,187,191,197,202,205,214

%N Numbers h such that antiharmonic mean B(h) of the numbers k < h such that gcd(k, h) = 1 is integer.

%C Numbers h such that B(h) = A053818(h) / A023896(h) = A175505(h) / A175506(h) is integer. Numbers h such that A175506(h) = 1. Complement of A179872. See A179873 (odd positive integers) for corresponding values A175505(a(n)). a(n) = union A003627 (primes of form 3n-1) and A179887.

%H Ivan Neretin, <a href="/A179871/b179871.txt">Table of n, a(n) for n = 1..2500</a>

%e Example: a(9) = 29 because B(29) = A053818(29) / A023896(29) = 7714/406 = 19 (integer).

%t B[n_] := Plus @@ ((ks = Select[Range[n], GCD[n, #] == 1 &])^2)/Plus @@ ks; Select[Range[215], IntegerQ[B[#]] &] (* _Ivan Neretin_, May 22 2015 *)

%Y Cf. A179872, A179873, A179874, A179875, A179876, A179877, A179878, A179879, A179880, A179882, A179883, A179884, A179885, A179886, A179887, A179890, A179891.

%K nonn

%O 1,2

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