cp's OEIS Frontend

A179891 Composites h such that antiharmonic mean B(h) of the numbers k < h such that gcd(k, h) = 1 is not integer.

%I A179891 #23 May 26 2025 09:56:53
%S A179891 4,6,8,9,12,14,15,16,18,20,21,24,25,26,27,28,30,32,33,35,36,38,39,40,
%T A179891 42,44,45,48,49,50,51,52,54,56,57,60,62,63,64,65,66,68,69,70,72,74,75,
%U A179891 76,77,78,80,81,84,86,87,88,90,92,93,95,96,98,99,100,102,104,105,108,111
%N A179891 Composites h such that antiharmonic mean B(h) of the numbers k < h such that gcd(k, h) = 1 is not integer.
%C A179891 Composites h such that B(h) = A053818(h) / A023896(h) = A175505(h) / A175506(h) is not integer.
%C A179891 Composites h such that A175506(h) > 1.
%C A179891 Subsequence of A179872.
%C A179891 A179872 is the union of this sequence and A007645.
%H A179891 Amiram Eldar, <a href="/A179891/b179891.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1749 from G. C. Greubel)
%e A179891 a(6) = 14 because B(14) = A053818(14) / A023896(14) = 406/42 = 29/3 (not integer).
%t A179891 f[n_] := 2 Plus @@ (Select[ Range@n, GCD[ #, n] == 1 &]^2)/(n*EulerPhi@n); Select[ Range@ 111, ! PrimeQ@# && ! IntegerQ@f@# &] (* _Robert G. Wilson v_, Aug 02 2010 *)
%o A179891 (PARI) isok(k) = if(isprime(k), 0, my(f = factor(k)); if(k == 1, 0, denominator(2*k/3 + (1/3) * prod(i = 1, #f~, 1 - f[i, 1])/eulerphi(f)) > 1)); \\ _Amiram Eldar_, May 25 2025
%Y A179891 Cf. A007645, A023896, A053818, A175505, A175506.
%Y A179891 Cf. A179871, A179872, A179873, A179874, A179875, A179876, A179877, A179878, A179879, A179880, A179882, A179883, A179884, A179885, A179886, A179887, A179890.
%K A179891 nonn
%O A179891 1,1
%A A179891 _Jaroslav Krizek_, Jul 30 2010
%E A179891 More terms from _Robert G. Wilson v_, Aug 02 2010