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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Corresponding values of numbers h+1 see A179878. Subsequence of A179875, A179871 and A179883.
LINKS
FORMULA
a(n) = (3*A179882(n) - 1)/2. - Hilko Koning, Aug 01 2018
EXAMPLE
From Michael De Vlieger, Jul 30 2018: (Start)
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
Sequence in context: A157917 A242234 A104867 * A216048 A079861 A014008
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jul 30 2010, Jul 31 2010
EXTENSIONS
More terms from Michael De Vlieger, Jul 30 2018
STATUS
approved

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Last modified April 20 17:12 EDT 2024. Contains 371845 sequences. (Running on oeis4.)