

A179877


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).


17



1, 10, 22, 46, 58, 82, 106, 166, 178, 226, 262, 265, 346, 358, 382, 454, 466, 469, 478, 493, 502, 505, 517, 562, 586, 589, 718, 781, 838, 862, 886, 889, 901, 910, 934, 982, 985, 1018, 1165, 1177, 1186, 1234, 1282, 1294, 1306, 1318, 1333, 1357, 1366, 1393
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OFFSET

1,2


COMMENTS



LINKS



FORMULA



EXAMPLE

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.
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]


MATHEMATICA

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]]]


CROSSREFS

Cf. A179871, A179872, A179873, A179874, A179875, A179876, A179878, A179879, A179880, A179882, A179883, A179884, A179885, A179886, A179887, A179890, A179891.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



