cp's OEIS Frontend

A179887 Nonprimes q such that antiharmonic mean B(q) of the numbers k < q such that gcd(k, q) = 1 is an integer, where B(q) = A053818(q) / A023896(q) = A175505(q) / A175506(q).

%I A179887 #25 May 26 2025 01:56:23
%S A179887 1,10,22,34,46,55,58,82,85,91,94,106,110,115,118,133,142,145,166,170,
%T A179887 178,182,187,202,205,214,217,226,230,235,247,253,259,262,265,266,274,
%U A179887 290,295,298,301,319,334,346,355,358,374,382,391,394,403,410,415,427
%N A179887 Nonprimes q such that antiharmonic mean B(q) of the numbers k < q such that gcd(k, q) = 1 is an integer, where B(q) = A053818(q) / A023896(q) = A175505(q) / A175506(q).
%C A179887 Nonprimes q such that A175506(q) = 1.
%C A179887 Subsequence of A179871.
%C A179887 A179871 is the union of this sequence and A003627.
%C A179887 Corresponding values of B(q) in A179890.
%H A179887 Amiram Eldar, <a href="/A179887/b179887.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1653 from G. C. Greubel)
%e A179887 a(6) = 55 because B(55) = A053818(55) / A023896(55) = 40700 / 1100 = 37 (integer).
%t A179887 f[n_] := 2 Plus @@ (Select[ Range@n, GCD[ #, n] == 1 &]^2)/(n*EulerPhi@n); Select[ Range@ 433, ! PrimeQ@# && IntegerQ@ f@# &] (* _Robert G. Wilson v_, Aug 02 2010 *)
%o A179887 (PARI) isok(k) = if(isprime(k), 0, my(f = factor(k)); if(k == 1, 1, denominator(2*k/3 + (1/3) * prod(i = 1, #f~, 1 - f[i, 1])/eulerphi(f)) == 1)); \\ _Amiram Eldar_, May 26 2025
%Y A179887 Cf. A003627, A023896, A053818, A175505, A175506.
%Y A179887 Cf. A179871, A179872, A179873, A179874, A179875, A179876, A179877, A179878, A179879, A179880, A179882, A179883, A179884, A179885, A179887, A179890, A179891.
%K A179887 nonn
%O A179887 1,2
%A A179887 _Jaroslav Krizek_, Jul 30 2010, Jul 31 2010
%E A179887 More terms from _Robert G. Wilson v_, Aug 02 2010