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A179876
Numbers h such that h and h-1 have same antiharmonic mean of the numbers k < h such that gcd(k, h) = 1.
19
2, 7, 11, 23, 47, 59, 66, 70, 78, 83, 107, 130, 167, 179, 186, 195, 211, 222, 227, 238, 255, 263, 266, 310, 322, 331, 347, 359, 366, 383, 399, 418, 438, 455, 463, 467, 470, 474, 479, 483, 494, 498, 503
OFFSET
1,1
COMMENTS
Corresponding values of numbers h-1 see A179875.
Numbers h such that A175505(h) = A175505(h-1).
Numbers h such that A175506(h) = A175506(h-1).
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).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2047 from R. J. Mathar)
EXAMPLE
For n=3: a(3) = 11; B(11) = A175505(11) / A175506(11) = 7, B(10) = A175505(10) / A175506(10) = 7.
MAPLE
antiHMeanGcd := proc(h)
option remember;
local a023896, a053818, k ;
a023896 := 0 ;
a053818 := 0 ;
for k from 1 to h do
if igcd(k, h) = 1 then
a023896 := a023896+k ;
a053818 := a053818+k^2 ;
end if;
end do:
a053818/a023896 ;
end proc:
n := 1:
for h from 2 do
if antiHMeanGcd(h) = antiHMeanGcd(h-1) then
printf("%d %d\n", n, h) ;
n := n+1 ;
end if;
end do: # R. J. Mathar, Sep 26 2013
MATHEMATICA
hmax = 1000;
antiHMeanGcd[h_] := antiHMeanGcd[h] = Module[{num = 0, den = 0, k}, For[k = 1, k <= h, k++, If[GCD[k, h] == 1, den += k; num += k^2]]; num/den];
Reap[n = 1; For[h = 2, h <= hmax, h++, If[antiHMeanGcd[h] == antiHMeanGcd[h - 1], Sow[h]; n++]]][[2, 1]] (* Jean-François Alcover, Mar 23 2020, after R. J. Mathar *)
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jul 30 2010, Jul 31 2010
STATUS
approved