%I #27 Sep 14 2018 04:32:43

%S 1,10,22,46,58,82,106,166,178,226,262,265,346,358,382,454,466,469,478,

%T 493,502,505,517,562,586,589,718,781,838,862,886,889,901,910,934,982,

%U 985,1018,1165,1177,1186,1234,1282,1294,1306,1318,1333,1357,1366,1393

%N Numbers h such that h and h+1 have same contraharmonic mean of the numbers k < h such that gcd(k, h) = 1 and simultaneously this mean is integer (see A179882).

%C Corresponding values of numbers h+1 see A179878. Subsequence of A179875, A179871 and A179883.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Contraharmonic_mean">Contraharmonic mean</a>

%F a(n) = (3*A179882(n) - 1)/2. - _Hilko Koning_, Aug 01 2018

%e From _Michael De Vlieger_, Jul 30 2018: (Start)

%e 10 is in the sequence since the reduced residue system of 10 is {1, 3, 7, 9} and that of 11 is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, the mean of the squares of these 2 systems, divided by the mean of the systems themselves, is 7 in both cases.

%e 6 is not in the sequence, because though the RRS of 6, {1, 5}, and that of 7, {1, 2, 3, 4, 5, 6}, have the same contraharmonic mean of 13/3, it is not integral. (End) [corrected by _Hilko Koning_, Aug 20 2018]

%t With[{s = Partition[Table[Mean[#^2]/Mean[#] &@ Select[Range[n - 1], GCD[#, n] == 1 &], {n, 1400}], 2, 1]}, Position[s, _?(And[IntegerQ@ First@ #, SameQ @@ #] &), 1, Heads -> False][[All, 1]]]

%Y Cf. A179871, A179872, A179873, A179874, A179875, A179876, 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

%E More terms from _Michael De Vlieger_, Jul 30 2018