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Numbers h such that h and h+1 have same antiharmonic mean of the numbers k < h such that gcd(k, h) = 1.
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%I #13 Mar 06 2021 06:24:12

%S 1,6,10,22,46,58,65,69,77,82,106,129,166,178,185,194,210,221,226,237,

%T 254,262,265,309,321,330,346,358,365,382,398,417,437,454,462,466,469,

%U 473,478,482,493,497,502

%N Numbers h such that h and h+1 have same antiharmonic mean of the numbers k < h such that gcd(k, h) = 1.

%C Corresponding values of numbers h+1 see A179876.

%C Numbers h such that A175505(h) = A175505(h+1).

%C numbers h such that A175506(h) = A175506(h+1).

%C Antiharmonic mean B(h) of numbers k such that gcd(k, h) = 1 for numbers h >= 1 and k < h = A053818(n) / A023896(n) = A175505(h) / A175506(h).

%C Conjecture: also numbers k such that mu(k) = 1 and mu(k+1) = -1, where mu is the Möbius function (tested on the first 10^4 terms). - _Amiram Eldar_, Mar 06 2021

%H Amiram Eldar, <a href="/A179875/b179875.txt">Table of n, a(n) for n = 1..10000</a>

%e For n=3: a(3) = 10; B(10) = A175505(10) / A175506(10) = 7, B(11) = A175505(11) / A175506(11) = 7.

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