A179871 Numbers h such that antiharmonic mean B(h) of the numbers k < h such that gcd(k, h) = 1 is an integer.

1, 2, 5, 10, 11, 17, 22, 23, 29, 34, 41, 46, 47, 53, 55, 58, 59, 71, 82, 83, 85, 89, 91, 94, 101, 106, 107, 110, 113, 115, 118, 131, 133, 137, 142, 145, 149, 166, 167, 170, 173, 178, 179, 182, 187, 191, 197, 202, 205, 214

Offset: 1

Author

Jaroslav Krizek, Jul 30 2010, Jul 31 2010

Keywords

• nonn

Comments

Numbers h such that B(h) = A053818(h) / A023896(h) = A175505(h) / A175506(h) is an integer.

Numbers h such that A175506(h) = 1.

Complement of A179872.

See A179873 (odd positive integers) for corresponding values A175505(a(n)).

Union of A003627 (primes of form 3n-1) and A179887.

Examples

			a(9) = 29 because B(29) = A053818(29) / A023896(29) = 7714/406 = 19 (integer).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from Ivan Neretin)

Crossrefs

Cf. A179872, A179873, A179874, A179875, A179876, A179877, A179878, A179879, A179880, A179882, A179883, A179884, A179885, A179886, A179887, A179890, A179891.

Programs

Mathematica

B[n_] := Plus @@ ((ks = Select[Range[n], GCD[n, #] == 1 &])^2)/Plus @@ ks; Select[Range[215], IntegerQ[B[#]] &] (* Ivan Neretin, May 22 2015 *)

PARI

isok(k) = {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 24 2025